Laminated Composite Doubly-Curved Shell Structures

Transcription

1

2 Francesco Tornabene Nicholas Fantuzzi Michele Bacciocchi Erasmo Viola Laminated Composite Doubly-Curved Shell Structures Differential and Integral Quadrature Strong Formulation Finite Element Method Volume II

3 Editor in chief: Scientific Committee: Chief assistant: First edition: Publishing Manager: Editorial Staff:

4 This Book is dedicated to all our opposers

5

6 About the Authors San Luigi Friction Clutch for High Performance Vehicles Mechanical Engineering Structural Mechanics Dynamic Behavior of Cylindrical Shells: Formulation and Solution Structural Mechanics Carlo Felice Jodi Structural Mechanics Scienza delle Costruzioni Structural Mechanics Scienza delle Costruzioni Structural Mechanics Structural Mechanics Modeling and Solution of Shell Structures Made of Anisotropic MaterialsUnified Formulation of Shell Structures Made of Anisotropic Materials. Numerical Analysis Using the Generalized Differential Quadrature Method and the Finite Element Method Mechanical Design and Laboratory Senior Design for Recycling Methodologies Applied to the Nautical Field Advanced Numerical Schemes for Anisotropic Materials Mechanics of Shell Structures Made of Composite Materials. The Generalized Differential Quadrature MethodMechanics of Laminated Composite Doubly-Curved Shell Structures. The Generalized Differential Quadrature Methodand the Strong Formulation Finite Element Method Journal of Computational EngineeringInternational Scholarly Research Notices Advances in Aircraft and Spacecraft ScienceMathematical Problems in Engineering Curved and Layered Structures Center for Studies and Research on the Identification of Materials and Structures Laminated Composite Doubly-Curved Shell Structures

7 Augusto Righi Civil Engineering Structural Engineering On the Behavior of Cylindrical Vaults Civil EngineeringStructural Engineering Curvature Effect on the Behavior of Shells with Anisotropic Material. Structural Engineering and Hydraulics Structural Engineering and Hydraulics Generalized Differential Quadrature Finite Element Method Applied to Advanced Structural MechanicsAbout Shell Structures Made of Anisotropic Materials. Unified Formulation and Numerical Analysis ICCS17 Ian Marshall's Award for Best Student Paper Static Analysis of Doubly-Curved Anisotropic Shells and Panels Using CUF Approach, Differential Geometry and Differential Quadrature Method Composite Structures Second Level Master Design of Oil & Gas plants Center for Studies and Research on the Identification of Materials and Structures Curved and Layered Structures F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

8 Civil Engineering Static analysis of the slab floor of the Torraccia ChurchCivil EngineeringStructural Engineering Higher-order Theories for Anisotropic Doubly- Curved Structures Civil, Chemical, Environmental, and Materials Engineering Civil, Chemical, Environmental, and Materials Engineering : Innovative theories for static and dynamic analysis of doubly-curved structures made of anisotropic materials: theoretical aspects and numerical solutions through the generalized differential quadrature method Structural Mechanics Plates and Shells M Theory of Structures M Curved and Layered Structures Structural and Computational Mechanics Book Series Laminated Composite Doubly-Curved Shell Structures

9 Structural MechanicsTheory of StructuresDynamics of Structures Structural Mechanics Structural Engineering and Hydraulics Centre of Studies and Research for the Identification of Materials and Structures - Michele Capurso Structural Durability and Health Monitoring Structural Engineering and MechanicsCurved and Layered Structures F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

10 Index Expansion of a generic function Expansion of an even function Expansion of an odd function Bellman approach First Bellman approach Second Bellman approach Quan and Chang approach Laminated Composite Doubly-Curved Shell Structures

11 Index Shu generalized approach Weighting coefficients for the second order derivatives Quan and Chang approach Shu generalized approach Coefficients of the higher order derivatives: recursive formulae Jacobi polynomials Gegenbauer polynomials Legendre polynomials Lobatto polynomials Chebyshev polynomials of the first kind Chebyshev polynomials of the second kind Chebyshev polynomials of the third kind Chebyshev polynomials of the fourth kind Hermite polynomials F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

12 Index Generalized Laguerre polynomials Equivalent Single Layer approach Layer-Wise approach Laminated Composite Doubly-Curved Shell Structures

13 Index Isotropic free-form shells and panels Comparison between theory of mixture and Mori-Tanaka scheme Weibull distribution Exponential distribution Curved free-form cylinder with variable thickness Convergence, accuracy and stability features of the LGDQ method Equivalent Single Layer approach Layer-Wise approach F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

14 Index Rectangular plate Doubly-curved laminated FG panels Free-form doubly-curved laminated FG shells Plane strain state Plane stress state Laminated Composite Doubly-Curved Shell Structures

15 Index Rectangular membrane Elliptic and circular membrane Highly concave membrane L-Shaped membrane Square membrane with a rhombic hole Trapezoidal membrane Triangular membrane Not homogeneous rectangular membrane Rectangular membrane with not homogeneous inclusion Arbitrarily shaped membrane with inclusion F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

16 Index Laminated Composite Doubly-Curved Shell Structures

17

18 Preface Laminated Composite Doubly-Curved Shell Structures Polynomial Differential Quadrature Harmonic Differential Quadrature basis functions Radial Basis Functions Laminated Composite Doubly-Curved Shell Structures

19 Preface a posteriori F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

20 Preface Differential Quadrature for Mechanics of Anisotropic Shells, Plates, Arches and Beams DiQuMASPAB Differential Quadrature for Mechanics of Anisotropic Shells, Plates, Arches and Beams DiQuMASPAB Meccanica delle Strutture a Guscio in Materiale Composito. Il Metodo Generalizzato di Quadratura Differenziale Mechanics of Shell Structures Made of Composite Materials. The Generalized Differential Quadrature Method Laminated Composite Doubly-Curved Shell Structures

21 Preface Center of Study and Research for the Identification of Materials and Structures F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

22 Bibliography The method of weighted residual: a review Differential quadrature method in computational mechanics Differential quadrature and long-term integration Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations Methods in Approximation Solution of Boundary-Value Problems by Orthogonal Collocation Numerical methods for the simulation of turbulence Solution of Differential Equation Models by Polynomial Approximation (Physical & Chemical Engineering Science) Orthogonal Polynomials and Special Functions Numerical Analysis of Spectral Methods. Theory and Applications Polynomial Approximation of Differential Equations Chebyshev and Fourier Spectral Methods Spectral Method. Fundamentals in Single Domains Numerical Approximation of Partial Differential Equations Laminated Composite Doubly-Curved Shell Structures

23 Bibliography Spectral Methods. Algorithms, Analysis and Applications Spectral Methods in Matlab An Introduction to the Mathematical Theory of Finite Elements Variational Methods in Theoretical Mechanics The Finite Element Method Finite Element Handbook Finite Element Analysis of Composite Laminates Origins, Milestones and Directions of the Finite Element Method - A Personal View Finite Elements: Their Design and Performance Finite Element Method with B-splines An Introduction to the Finite Element Method An Introduction to Nonlinear Finite Element Analysis Handbook of Computational Methods for Integration Structural Analysis with the Finite Element Method, Linear Static. Volume 1. Basis and Solids Spectral Element Method in Structural Dynamics Smoothed Finite Element Methods Finite Rotation Shells. Basic Equations and Finite Elements for Reissner Kinematics Guided Waves in Structures for SHM. The Time-Domain Spectral Element Method F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

24 Bibliography The least-squares finite element method: theory and applications in computational fluid dynamics and electromagnetics Structural Analysis with the Finite Element Method, Linear Static. Volume 2. Beams, Plates and Shells The Finite Element Method: Its Basis and Fundamentals A Unified Approach for Solving Nonlinear Partial Differential Equations in Chemical Engineering Applications Solution of Transport Phenomena Type Models by the Method of Differential Quadratures as Illustrated on the LNG Vapor Dispersion Process Modeling Application of differential quadrature to transport processes Solution of the Poisson equation by differential quadrature Differential quadrature for multi-dimensional problems On the solution of the Thomas-Fermi equation by differential equation Application of differential quadrature in solution of pool boiling in cavities Computational considerations in non-linear diffusion The method of differential quadrature for transient nonlinear diffusion Nonlinear analysis in chemical engineering Laminated Composite Doubly-Curved Shell Structures

25 Bibliography New insights in solving distributed system equations by the quadrature method - I. Analysis New insights in solving distributed system equations by the quadrature method - II. Numerical experiments Two new approximate methods for analyzing free vibration of structural components Nonlinear bending analysis of orthotropic rectangular plates by the method of differential quadrature The differential quadrature method for irregular domains and application for plate vibration Free vibration analysis of tapered rectangular plates by differential quadrature method: a semi-analytical approach Free vibration analysis of thin cylindrical shells by the differential quadrature method Differential quadrature for static and free vibration analyses of anisotropic plates Static and free vibrational analysis of beams and plates by differential quadrature method Convergence of DQ method in the analysis of anisotropic plates A New Approach for Structural Analysis. The Quadrature Element Method A new approach to the differential quadrature method for fourth-order equations F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

26 Bibliography High accuracy plane stress and plate element in the quadrature element method Development of a Differential Quadrature Technique for the Fundamental Frequency Analysis of Tapered, Orthotropic, Anisotropic and Laminated Thin Plates Application of Differential Quadrature to the Analysis of Structural Components Application of differential quadrature to static analysis of structural components Flexural-torsional buckling analysis of arches with warping using DQM Vibration analysis of shear deformable circular arches by the differential quadrature method Vibration and buckling analysis of circular arches using DQM Vibration analysis of horizontally curved beams with warping using DQM Differential Quadrature Method in Computational Mechanics. New Developments and Applications Vibration analysis of plates with curvilinear quadrilateral platforms by DQM using blending functions Static analysis of structures by the quadrature element method (QEM) Free vibration of plates by the high accuracy element method Harmonic differential quadrature method and applications to analysis of structural components Laminated Composite Doubly-Curved Shell Structures

27 Bibliography A new approach in applying differential quadrature to static and free vibrational analyses of beams and plates Free vibration analysis of annular plates by the DQ Method Differential quadrature analysis of deflection, buckling and free vibration of beams and rectangular plates Buckling and vibration analysis of skew plates by differential quadrature method Generalized differential-integral quadrature and application to the simulation of incompressible viscous flows including parallel computation Parallel simulation of incompressible viscous flows by generalized differential quadrature Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations A block-stodola eigensolution technique for large algebraic systems with non-symmetrical matrices Free vibration analysis of circular cylindrical shells Fundamental frequency of tapered plates by differential quadrature Letter to Editor. Comment on Application of generalized quadrature to solve two-dimensional incompressible Navier-Stokes Equations, by C. Shu and B.E. Richards F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

28 Bibliography Calculation and analysis of weighting coefficient matrices in differential quadrature method Differential quadrature method for high order boundary value problems Rapid and accurate solution of reactor models by the quadrature method Generalized differential and integral quadrature and their application to solve boundary layer equations Analysis of vibrating, thin, rectangular plates with point supports by the method of differential quadrature Vibrations of non-uniform rings studied by means of the differential quadrature method Analysis of vibrating circular plates of nonuniform thickness by the method of differential quadrature Free vibrations of a rotating multi-layered cylindrical shell Application of GDQ scheme to simulate incompressible viscous flows around complex geometries On free vibration analysis of circular annular plates with non-uniform thickness by the differential quadrature method Free vibration analysis of composite laminated conical shells by generalized differential quadrature An efficient approach for free vibration analysis of conical shells Laminated Composite Doubly-Curved Shell Structures

29 Bibliography Numerical studies of unsteady boundary layer flows past an impulsively started circular cylinder by GDQ and GIQ approaches Differential Quadrature Method and its Applications in Engineering The structures of the weighting coefficient matrices of the harmonic differential quadrature and its applications Differential quadrature method for thick symmetric cross-ply laminates with first-order shear flexibility Differential quadrature method for Mindlin plates on Winkler foundations On the DQ analysis of geometrically non-linear vibration of immovably simply-supported beams On the free vibration analysis of circular plates with stepped thickness over a concentric region by the differential quadrature element method Vibration analysis of a rotating truncated circular conical shell Nonlinear models and problems in applied sciences from differential quadrature to generalized collocation methods Implementation of clamped and simply supported boundary conditions in the GDQ free vibration analysis of beams and plates A generalized approach for implementation general boundary conditions in the GDQ free vibration analysis of plates F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

30 Bibliography Free vibration analysis of laminated composite cylindrical shells by DQM Fourier expansion-based differential quadrature and its application to Helmholtz eigenvalue problems An efficient approach for numerical simulation of flows in Czochralski crystal growth Explicit computation of weighting coefficients in the harmonic differential quadrature Vibration analysis of circular Mindlin plates using the differential quadrature method Solution of Nonlinear Evolution Problems by Parallelized Collocation- Interpolation Methods Lyapunov formulation for efficient solution of the Poisson and convection-diffusion equations by the differential quadrature method Analysis of annular Reissner-Mindlin plates using differential quadrature method Frequency characteristics of a thin rotating cylindrical shell using the generalized differential quadrature method Buckling of circular cylindrical shells by the differential quadrature method Analysis of eccentrically stiffened plates with mixed boundary conditions using differential quadrature method Differential quadrature method: application to initial-boundary-value problems Laminated Composite Doubly-Curved Shell Structures

31 Bibliography Comparison of two approaches for implementing stream function boundary conditions in DQ simulation of natural convection in a square cavity On the performance of three iterative methods for solution of GDQ algebraic equations Different interface approximations in multi-domain GDQ simulation of Czochralski bulk flows On the equivalence of generalized differential quadrature and highest order finite difference scheme Static and free vibrational analysis of rectangular plates by the differential quadrature element method Static analysis of Reissner-Mindlin plates by differential quadrature element method Differential quadrature element method for static analysis of Reissner-Mindlin polar plates Free vibration analysis of Mindlin sector plates: numerical solutions by differential quadrature method Differential quadrature element method: a new approach for free vibration analysis of polar Mindlin plates having discontinuities Analysis of vibrating thick rectangular plates with mixed boundary constraints using differential quadrature element method Vibration analysis of discontinuous Mindlin plates by differential quadrature element method F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

32 Bibliography Domain decomposition and discretization of continuum mathematical models Axisymmetric free vibration of thick annular plates Three-dimensional vibration analysis of rectangular plates based on differential quadrature method Comparative accuracy of DQ and HDQ methods for three-dimensional vibration analysis of rectangular plates Vibrational analysis of toroidal panels using the differential quadrature method Solution of Helmholtz equation by differential quadrature method Application of multi-domain GDQ method to analysis of waveguides with rectangular boundaries Application of multi-domain GDQ method to analysis of waveguides with rectangular boundaries Vibration of thick rotating laminated composite cylindrical shells Application of differential quadrature method to simulate natural convection in a concentric annulus Treatment of mixed and nonuniform boundary conditions in GDQ vibration analysis of rectangular plates On optimal selection of interior points for applying discretized boundary conditions in DQ vibration analysis of beams and plates Laminated Composite Doubly-Curved Shell Structures

33 Bibliography Parametric instability of conical shells by the generalized differential quadrature method A differential quadrature procedure for three-dimensional buckling analysis of rectangular plates Differential Quadrature and Its Application in Engineering Orthogonal collocation on finite elements Spectral methods for problems in complex geometries Multi-domain spectral technique for viscous flow calculations A spectral element method for fluid dynamics: laminar flow in a channel expansion Spectral Methods. Evolution to Complex Geometries and Applications to Fluid Dynamics Guided Waves in Structures for SHM. The Time-Domain Spectral Element Method A modified quadrature element method to perform static analysis of structures Static analysis of a Bickford beam by means of the DQEM High-accuracy differential quadrature finite element method and its application to free vibrations of thin plate with curvilinear domain F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

34 Bibliography A weak form quadrature element method for plane elasticity problems A differential quadrature finite element method A differential quadrature analysis of dynamic and quasi-static magneto-thermo-elastic stresses in a conducting rectangular plate subjected to an arbitrary variation of magnetic field Weak form quadrature element analysis of Bickford Beams Buckling analysis of shear deformable plates using the quadrature element method Non-linear quadrature element analysis of planar frames based on geometrically exact beam theory Large deflection elasto-plastic analysis of frames using the weak-form quadrature element method Analysis of thin plates by the weak form quadrature element method Thickness-shear vibration analysis of rectangular quartz plates by a numerical extended Kantorovich method Static and free vibration analysis of rectangular plates by the new version of the differential quadrature element method Differential quadrature domain decomposition method for a class of parabolic equations Laminated Composite Doubly-Curved Shell Structures

35 Bibliography A differential quadrature as a numerical method to solve differential equations Axisymmetric bending solution of shells of revolution by the generalized differential quadrature rule Vibration analysis of beams using the generalized differential quadrature rule and domain decomposition In-plane vibration analyses of circular arches by the generalized differential quadrature rule Application of generalized differential quadrature rule in Blasius and Osanger equations Free vibration analysis of circular plates with variable thickness by the generalized differential quadrature rule The generalized differential quadrature rule for fourth-order differential equations Multipoint boundary value problems by differential quadrature method Differential quadrature solutions of eighth-order boundaryvalue differential equations Free vibration analysis of circular plates using generalized differential quadrature rule Application of the generalized differential quadrature rule to initial-boundary-value problems F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

36 Bibliography Rectangular thick plates on Winkler foundation: differential quadrature element solution A new differential quadrature methodology for beam analysis and the associated differential quadrature element method Application of a new differential quadrature methodology for free vibration analysis of plates An efficient differential quadrature methodology for free vibration analysis of arbitrary straight-sided quadrilateral thin plate New approaches in application of differential quadrature method to fourth-order differential equations Application of the differential quadrature method to two-dimensional problems with arbitrary geometry Vibration analysis of beams using the generalized differential quadrature rule and domain decomposition Discrete singular convolution methodology for free vibration and stability analyses of arbitrary straight-sided quadrilateral plates A four-node discrete singular convolution for geometric transformation and its application to numerical solution of vibration problem of arbitrary straight sided quadrilateral plates Vibration analysis of plates with curvilinear quadrilateral domains by discrete singular convolution method Laminated Composite Doubly-Curved Shell Structures

37 Bibliography A four-node differential quadrature method for straight sided quadrilateral Reissner/Mindlin plates An eight-node curvilinear differential quadrature formulation for Reissner/Mindlin plates Static analysis of Mindlin plates: the differential quadrature element method (DQEM) Free vibration analysis of curvilinear quadrilateral plates by the differential quadrature method Development of Differential Quadrature Methods and their Applications to plane Elasticity Advanced Differential Quadrature Methods Solution of Poisson and Laplace equations by quadrilateral quadrature element The warping torsion bar model of the differential quadrature element method The development of irregular elements for differential quadrature element method steady-state heat conduction analysis Adaptive differential quadrature element refinement analyses of fluids mechanics problems The differential quadrature element method irregular element torsion analysis model F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

38 Bibliography A generalized differential quadrature element method Vibration of prismatic beam on an elastic foundation by the differential quadrature element method Differential quadrature element analysis using extended differential quadrature Vibration of nonuniform shear deformable axisymmetric orthotropic circular plates solved by DQEM Differential quadrature finite difference method for structural mechanics problems DQEM and DQFDM for the analysis of composite two-dimensional elasticity problems Buckling equilibrium equations of arbitrarily loaded nonprismatic composite beams and the DQEM buckling analysis using EDQ Out-of-plane deflection of nonprismatic curved beams structures solved by the DQEM Extended GDQ and related discrete element analysis methods for transient analyses of continuum mechanics problems Dynamic Response of shear-deformable axisymmetric orthotropic circular plate structures solved by the DQEM and EDQ based time integration schemes DQEM and DQFDM irregular elements for analyses of 2-D heat conduction in orthotropic media DQEM analysis of in-plane vibration of curved beam structures Discrete Element Analysis Methods of Generic Differential Quadratures Laminated Composite Doubly-Curved Shell Structures

39 Bibliography Generalized Differential Quadrature Finite Element Method applied to Advanced Structural Mechanics Generalized differential quadrature finite element method for cracked composite structures of arbitrary shape Soft core plane state structures under static loads using GDQFEM and Cell Method GDQFEM numerical simulations of continuous media with cracks and discontinuities On Static Analysis of Plane State Structures via GDQFEM and Cell Method Generalized Differential Quadrature Finite Element Method for Vibration Analysis of Arbitrarily Shaped Membranes Exact and approximate dynamic analysis of circular arches using DQM The generalized quadrature method for frequency analysis of a rotating conical shell with initial pressure Thermal bending analysis of laminated orthotropic plates by the generalized differential quadrature method Influence of initial pressure on frequency characteristics of a rotating truncated circular conical shell Generalized differential quadrature method for frequency of rotating multilayered conical shell F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

40 Bibliography Differential quadrature method for vibration analysis of shear deformable annular sector plates Free vibration analysis of rotating circular cylindrical shells on elastic foundation Free vibration analysis of isosceles triangular Mindlin plates by the triangular differential quadrature Solutions of nonlinear problems in applied sciences by generalized collocation methods and mathematica Letters to the editor. Comments on Differential quadrature method for vibration analysis of shear deformable annular sector plates Solving initial value problems by differential quadrature method - part 1: first-order equations Solving initial value problems by differential quadrature method - part 2: second- and higher-order equations Orthotropic influence on frequency characteristics of rotating composite laminated conical shell by the generalized differential quadrature method Three-dimensional static solutions of rectangular plates by variant differential quadrature method Differential quadrature element method for buckling analysis of rectangular Mindlin plates having discontinuities Collocation methods with controllable dissipation for linear dynamics Laminated Composite Doubly-Curved Shell Structures

41 Bibliography Numerical study of grid distribution effect on accuracy of DQ analysis of beams and plates by error estimation of derivative approximation Numerical study of natural convection in an eccentric annulus between a square outer cylinder and a circular inner cylinder using DQ method On free vibration analysis of non-linear piezoelectric circular shallow spherical shells by the differential quadrature element method Differential quadrature solution for the three vibration analysis of laminated conical shells with variable stiffness A differential quadrature analysis of vibration for rectangular stiffened plates Triangular differential quadrature and its application to elastostatic analysis of Reissner plates Generalized differential quadrature for the beam with varying cross section On equivalence of the time domain differential quadrature method and the dissipative Runge-Kutta collocation method Stability and accuracy of differential quadrature method in solving dynamic problems Static and stability analyses of arbitrary straight-sided quadrilateral thin plates by DQM F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

42 Bibliography Generalized differential quadrature method for the free vibration of truncated conical panels Block-marching in time with DQ discretization: an efficient method for time-dependent problems Efficient computation of natural convection in a concentric annulus between an outer square cylinder and an inner circular cylinder Numerical simulation of natural convection in a square cavity by simple-generalized differential quadrature method Analysis of rectangular laminated composite plates via FSDT meshless method On non-linear behaviour of spherical shallow shells bonded with piezoelectric actuators by the differential quadrature element method (DQEM) Thermally induced dynamic instability of laminated composite conical shells A refined asymptotic theory of laminated conical shells Dynamic analysis of laminated composite plates using a layer-wise mixed finite element method Some theoretical aspects of generalized quadrature methods Imposition of boundary conditions by modifying the weighting coefficient matrices in the differential quadrature method Laminated Composite Doubly-Curved Shell Structures

43 Bibliography Generalized Lagrange functions and weighting coefficients formulae for the harmonic differential quadrature method Accurate free vibration analysis of completely free symmetric cross-ply rectangular laminated plates Shear deformation in thermal vibration analysis of laminated plates by the GDQ method Shear deformation in thermal bending analysis of laminated plates by the GDQ method A DQEM for vibration of shear deformable nonuniform beams with general boundary conditions DQM analysis of skewed and trapezoidal plates Three-dimensional modelling of elastic bonding in composite laminates layerwise differential quadrature Out-of-plane static analysis of circular arches by DQM A methodology for the generation of low-cost higherorder methods for linear dynamics Generalized differential quadrature method for the free vibration of rotating composite laminated conical shell with various boundary conditions Local radial basis function-based differential quadrature method and its application to solve two-dimensional incompressible Navier-Stokes equations F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

44 Bibliography Shear flexible element based on coupled displacement field for large deflection analysis of laminated plates Stability and accuracy of the iterative differential quadrature method Simulating non-linear coupled oscillators by an iterative differential quadrature method Buckling analyses of anisotropic plates and isotropic skew plates by the new version differential quadrature method Three-dimensional theory of elasticity for free vibration analysis of composite laminates via layerwise differential quadrature modelling Post-buckling analysis of imperfect laminates using finite strips based on a higher-order plate theory Two approaches to the dynamic analysis of foundation beams subjected to subtangential forces Application of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for buckling analysis of thin isotropic plates and elastic columns Buckling analysis of generally laminated composite plates (generalized differential quadrature rules versus Rayleigh-Ritz method) Simulation of incompressible viscous flows past a circular cylinder by hybrid FD scheme and meshless least square-based finite difference method Laminated Composite Doubly-Curved Shell Structures

45 Bibliography A semi-analytical method for free vibration of straight orthotropic beams with rectangular cross-sections A mixed method for bending and free vibration of beams resting on a Pasternak elastic foundation The application of special matrix product to differential quadrature solutions of geometrically nonlinear bending of orthotropic rectangular plates In-plane free vibration analysis of circular arches with varying cross-sections using differential quadrature method Vibration of non-uniform thick plates on elastic foundation by differential quadrature method Comparison of discrete singular convolution and generalized differential quadrature for the vibration analysis of rectangular plates Vibration analysis of a torus-cylinder shell assembly Re-analysis of free vibration of annular plates by the new version of differential quadrature method Free vibration analyses of thin sector plates by the new version of differential quadrature method Application of a new differential quadrature element method to free vibration analysis of beams and frame structures Asymptotic DQ solutions of functionally graded annular spherical shells F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

46 Bibliography Numerical simulation of natural convection between two elliptical cylinders using DQ method A Differential Quadrature Method Solution for Shear-Deformable Shells of Revolution Static Analysis of Shear-Deformable Shells via G.D.Q. Method Geometrically nonlinear analysis of doubly curved isotropic shells resting on elastic foundation by a combination of harmonic differential quadrature-finite difference methods Vibration analysis of edge-cracked beam on elastic foundation with axial loading using the differential quadrature method Rotating Shell Dynamics Three-dimensional analysis of coupled thermo-piezoelectro-mechanical behaviour of multilayered plates using differential quadrature technique Polynomial and harmonic differential quadrature methods for free vibration of variable thickness thick skew plates Free vibration analysis of variable thickness thin and moderately thick plates with elastically restrained edges by DQM Buckling analysis of an orthotropic thin shell of revolution using differential quadrature The G.D.Q. Method for the Harmonic Dynamic Analysis of Rotational Shell Structural Elements Laminated Composite Doubly-Curved Shell Structures

47 Bibliography Analytical and Differential Quadrature Results for Vibration Analysis of Damaged Circular Arches Vibration analysis of damaged circular arches with varying cross-section Natural frequencies and mode shapes for an orthotropic thin shell of revolution A highly accurate linearized method for free boundary problems A multidomain differential quadrature approach to plane elastic problems with material discontinuities Free Vibration Analysis of Spherical Caps using G.D.Q. Numerical Solution Harmonic differential quadrature-finite differences coupled approaches geometrically nonlinear static and dynamic analysis of rectangular plates on elastic foundation An efficient method for free vibration analysis of rotating truncated conical shells Hierarchical higher-order dissipative methods for transient analysis DQM free vibration analysis of moderately thick symmetric laminated plates with elastically restrained edges Differential quadrature nonlinear analysis of skew composite plates based on FSDT Three-dimensional free vibration analysis of inhomogeneous thick orthotropic shells of revolution using differential quadrature F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

48 Bibliography Vibration analysis of conical shell structures using GDQ Method Natural frequencies of an orthotropic thin toroidal shell of elliptical cross-section Theoretical natural frequencies and mode shapes for thin and thick curved pipes and toroidal shells Generalized Collocation Methods: Solution to Nonlinear Problems Nonlinear analysis of thin rectangular plates on Winkler-Pasternak elastic foundation differential by DSC-HQM methods Dynamic analysis of composite shells using differential quadrature method Modellazione e Soluzione di Strutture a Guscio in Materiale Anisotropo Vibration analysis of spherical structural elements using the GDQ Method Analytical and numerical results for vibration analysis of multi-stepped and multi-damaged circular arches Dynamical analysis of spherical shell structural elements using the First Order Shear Deformation TheoryMechanical Vibration: where do we stand? Nonlinear stability analysis of thin doubly curved orthotropic shallow shells by the differential quadrature method Nonconservative stability problems via Generalized Differential Quadrature Method Laminated Composite Doubly-Curved Shell Structures

49 Bibliography 2-D solution for free vibrations of parabolic shells using Generalized Differential Quadrature Method 2-D Differential Quadrature solution for vibration analysis of functionally graded conical, cylindrical and annular shell structures Free Vibration analysis of functionally graded conical, cylindrical shell and annular plate structures with a four-parameter power-law distribution Free vibration analysis of functionally graded panels and shells of revolution Free vibrations of four-parameter functionally graded parabolic panels and shell of revolution Free vibrations of three parameter functionally graded parabolic panels of revolution Critical flow speeds of pipes conveying fluid by the Generalized Differential Quadrature Method Free vibrations of laminated composite doubly-curved shells and panels of revolution via the GDQ Method 2-D GDQ solution for free vibrations of anisotropic doubly-curved shells and panels of revolution Free vibrations of anisotropic doubly-curved shells and panels of revolution with a free-form meridian resting on Winkler-Pasternak elastic foundations FGM and laminated doubly-curved shells and panels of revolution with a free-form meridian: a 2-D GDQ solution for free vibrations F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

50 Bibliography Meccanica delle Strutture a Guscio in Materiale Composito. Il metodo Generalizzato di Quadratura Differenziale Laminated composite rectangular and annular plates: a GDQ solution for static analysis with a posteriori shear and normal stress recovery Static analysis of laminated composite curved shells and panels of revolution with a posteriori shear and normal stress recovery using Generalized Differential Quadrature Method General anisotropic doubly-curved shell theory: a Differential Quadrature solution for free vibrations of shells and panels of revolution with a free-form meridian Numerical investigation of functionally graded cylindrical shells and panels using the generalized unconstrained third order theory coupled with the stress recovery Analysis of sandwich plates by generalized differential quadrature method Free-form laminated doubly-curved shells and panels of revolution resting on Winkler-Pasternak elastic foundations: a 2-D GDQ solution for static and free vibration analysis Mixed static and dynamic optimization of four-parameter functionally graded completely doubly-curved and degenerate shells and panels using GDQ method FGM and laminated doubly-curved and degenerate shells resting on nonlinear elastic foundations: a GDQ solution for static analysis with a posteriori stress and strain recovery Static analysis of functionally graded doubly-curved shells and panels of revolution Laminated Composite Doubly-Curved Shell Structures

51 Bibliography General higher-order equivalent single layer theory for free vibrations of doubly-curved laminated composite shells and panels General higher-order shear deformation theories for the free vibration analysis of completely doubly-curved laminated shells and panels Static analysis of completely doubly-curved laminated shells and panels using general higher-order shear deformation theories Free vibration analysis of multiple-stepped beams by the differential quadrature element method Weak form quadrature element analysis of planar slender beams based on geometrically exact beam theory Strong Formulation Finite Element Method for Arbitrarily Shaped Laminated Plates Part I. Theoretical Analysis Strong Formulation Finite Element Method for Arbitrarily Shaped Laminated Plates Part II. Numerical Analysis Analysis of thick isotropic and cross-ply laminated plates by generalized differential quadrature method and a unified formulation Mechanics of Laminated Composite Doubly-Curved Shell Structures. The Generalized Differential Quadrature Method and the Strong Formulation Finite Element Method Static analysis of doubly-curved anisotropic shells and panels using CUF approach, differential geometry and differential quadrature method F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

52 Bibliography Winkler-Pasternak foundation effect on the static and dynamic analyses of laminated doubly-curved and degenerate shells and panels Static Analysis of Functionally Graded Conical Shells and Panels Using the Generalized Unconstrained Third Order Theory Coupled with the Stress Recovery Multiquadrics - A scattered data approximation scheme with applications to computational fluid-dynamics - I surface approximations and partial derivative estimates Multiquadrics - A scattered data approximation scheme with applications to computational fluid-dynamics - II solutions to parabolic, hyperbolic and elliptic partial differential equations Solving differential equations with radial basis functions: multilevel methods and smoothing Meshfree Approximation Methods with Matlab On choosing optimal shape parameters for RBF approximation Computation of natural frequencies of shear deformable beams and plates by an RBF-pseudospectral method Static deformations and vibration analysis of composite and sandwich plates using a layerwise theory and RBF-PS discretizations with optimal shape parameter An algorithm for selecting a good value for the parameter c in radial basis function interpolation Laminated Composite Doubly-Curved Shell Structures

53 Bibliography Meshless Galerkin methods using radial basis functions Radial basis functions On the optimal shape parameters of radial basis functions used for 2-D meshless methods Analysis of composite plates using higher-order shear deformation theory and a finite point formulation based on the multiquadric radial basis function method Solution of partial differential equations by a global radial basis function-based differential quadrature method, Free vibration analysis of symmetric laminated composite plates by FSDT and radial basis functions Analysis of composite plates by trigonometric shear deformation theory and multiquadrics Modelling of composite and sandwich plates by a trigonometric layerwise deformation theory and radial basis functions Numerical computation of three-dimensional incompressible viscous flows in the primitive variable form by local multiquadratic differential quadrature method Mesh-free radial basis function method for static, free vibration and buckling analysis of shear deformable composite laminates Vibration analysis of arbitrarily shaped membranes using local radial basis function-based differential quadrature method F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

54 Bibliography Natural frequencies of generally laminated composite plates using the Gaussian radial basis function and first-order shear deformation theory RBF-FD formulas and convergence properties Thin plate spline radial basis functions for vibration analysis of clamped laminated composite plates Optimal constant shape parameter for multiquadric based RBF-FD method Thin plate spline radial basis function for the free vibration analysis of laminated composite shells Comparison of three spectral methods for the Benjamin-Ono equation: Fourier pseudospectral, rational Christov functions and Gaussian radial basis functions Analysis of laminated shells by a sinusoidal shear deformation theory and radial basis functions collocation, accounting for through-the-thickness deformations A local radial basis functions - Finite differences technique for the analysis of composite plates Buckling and vibration of isotropic and laminated plates by radial basis functions Free vibration analysis of functionally graded annular plates by state-space based differential quadrature method and comparative modeling by ANN A quasi-3d sinusoidal shear deformation theory for the static and Laminated Composite Doubly-Curved Shell Structures

55 Bibliography free vibration analysis of functionally graded plates Transient dynamic and free vibration analysis of functionally graded truncated conical shells with non-uniform thickness subjected to mechanical shock loading A quasi-3d hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates A novel algorithm for shape parameter selection in radial basis functions collocation method Radial basis functions collocation for the bending and free vibration analysis of laminated plates using the Reissner-Mixed Variational Theorem Free vibration analysis of functionally graded shells by a higherorder shear deformation theory and radial basis functions collocation, accounting for through-the-thickness deformations On optimization of the RBF shape parameter in a grid-free local scheme for convection dominated problems over nonuniform centers Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3d higher-order shear deformation theory and a meshless technique Radial basis function method applied to doubly-curved laminated composite shells and panels with a general F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

56 Bibliography higher-order equivalent single layer theory Numerical solution of the system of second-order boundary value problem using the local radial basis functions based differential quadrature collocation method Energy based approach for shape parameter selection in radial basis functions collocation method Simulation of natural convection in eccentric annuli between a square outer cylinder and a circular inner cylinder using local MQ- DQ method Numerical simulation of joule heating phenomenon using meshless RBF-DQ method Local RBF-DQ method for two-dimensional transient heat conduction problems Local RBF-based differential quadrature collocation method for the boundary layer problems Unsteady seepage analysis using local radial basis function-based differential quadrature method Numerical simulation of electric field in complex geometries for different electrode arrangements using meshless local MQ-DQ method Laminated Composite Doubly-Curved Shell Structures

57 Bibliography Meshless local RBF- DQ for 2-D heat condution: a comparative study Unsteady seepage analysis using local radial basis function-based differential quadrature method Entropy generation due to natural convection in a partially heated cavity by local RBF-DQ method Radial basis functions-differential quadrature collocation and a unified formulation for bending, vibration and buckling analysis of laminated plates, according to Murakami s Zig-Zag theory Numerical solution of stokes flow in a circular cavity using mesh-free local RBF-DQ A hybrid DQ/LMQRBF-DQ approach for numerical solution of Poisson-type and Burger's equations in irregular domain Numerical modeling of long waves in shallow water using LRBF-DQ and hybrid DQ/LRBF-DQ The solitary wave solution of coupled Klein Gordon Zakharov equations via two different numerical methods RBF-DQ solution for shallow water equations A novel upwind-based local radial basis function differential quadrature method for convection-dominated flows F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

58 Bibliography Numerical comparison of least square-based finitedifference (LSFD) and radial basis function-based finite-difference (RBFFD) methods A local radial basis functions- Finite differences technique for the analysis of composite plates Radial basis functions-finite differences collocation and a unified formulation for bending, vibration and buckling analysis of laminated plates, according to Murakami s zig-zag theory Analysis of thick plates by local radial basis functions-finite differences method Solution to PDEs using radial basis function finite-differences (RBF-FD) on multiple GPUs Numerical modeling of long waves in shallow water using Incremental Differential Quadrature Method Numerical modelling of water hammer using differential quadrature method A differential quadrature analysis of unsteady open channel flow Tidal and surge modelling using differential quadrature: a case study in the Bristol channel Local adaptive differential quadrature for free vibration analysis of cylindrical shells with various boundary conditions Laminated Composite Doubly-Curved Shell Structures

59 Bibliography On the accuracy and stability of a variety of differential quadrature formulations for the vibration analysis of beams A local adaptive differential quadrature method for multi-dimensional inverse scattering problem of wave propagation A local adaptive differential quadrature method for solving multi-dimensional heat transport equation at the microscale Identification of crack locations and depths in a multi-cracks beam by using local adaptive differential quadrature method Upwind local differential quadrature method for solving incompressible viscous flow A localized differential quadrature (LDQ) method and its application to the 2D wave equation A numerical study of wave propagation in a poroelastic medium by use of localized differential quadrature method Local differential quadrature method for 2-D flow and forced-convection problems in irregular domains The localized differential quadrature method for two-dimensional stream function formulation of Navier-Stokes equations Numerical modelling of the mild slope equation using localised differential quadrature method F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

60 Bibliography Vibration analysis of structural elements using differential quadrature method Generation of inflow turbulence using the local differential quadrature method Buckling analyses of axially functionally graded nonuniform columns with elastic restraint using a localized differential quadrature method Bernstein differential quadrature method for solving the unsteady state convection-diffusion equation Solutions of 2nd-order linear differential equations subject to Dirichlet boundary conditions in a Bernstein polynomial basis The Local GDQ Method Applied to General Higher-Order Theories of Doubly-Curved Laminated Composite Shells and Panels: the Free Vibration Analysis Three-dimensional temperature dependent free vibration analysis of functionally graded material curved panels resting on two-parameter elastic foundation using a hybrid semi-analytic, differential quadrature method A semi-analytical threedimensional free vibration analysis of functionally graded curved panels A mixed Ritz-DQ method for forced vibration of functionally graded beams carrying moving loads A mixed method for free and forced vibration of rectangular plates Laminated Composite Doubly-Curved Shell Structures

61 Bibliography Modified mixed Ritz-DQ formulation for free vibration of thick rectangular and skew plates with general boundary conditions A simple and accurate mixed FE-DQ formulation for free vibration of rectangular and skew Mindlin plates with general boundary conditions Discrete singular convolution for the solution of the Fokker-Planck equation Discrete singular convolution for the sine-gordon equation Solving quantum eigenvalue problems by discrete singular convolution Wavelets generated by using discrete singular convolution kernels Numerical solution of incompressible Euler and Navier- Stokes equations by efficient discrete singular convolution method Discrete singular convolution for beam analysis Vibration analysis by discrete singular convolution A new algorithm for solving some mechanical problems The determination of the natural frequencies of rectangular plates with mixed boundary conditions by discrete singular convolution A new benchmark quality solution for the buoyancy driven cavity by discrete singular convolution F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

62 Bibliography A novel approach for the analysis of high frequency vibrations Discrete singular convolution for the prediction of high frequency vibration of plates Comparison of the discrete singular convolution algorithm and the Fourier pseudospectral methods for solving partial differential equations Numerical solution of incompressible flows by the discrete singular convolution A comparison of the spectral and the discrete singular convolution schemes for the KdV-type equations Discrete singular convolution and its application to the analysis of plates with internal supports, I Theory and algorithm Discrete singular convolution and its application to the analysis of plates with internal supports. II Complex supports Comparison of the discrete singular convolution and three other numerical schemes for Fisher's equation Discrete singular convolution for the prediction of high frequency vibration of plates Comparison of discrete singular convolution and generalized differential quadrature for the vibration analysis of rectangular plates ption valuation by using discrete singular convolution Laminated Composite Doubly-Curved Shell Structures

63 Bibliography A proof that the discrete singular convolution (DSC)/Lagrange-distributed approximating function (LDAF) method is inferior to high order finite differences On the validity of A proof that the discrete singular convolution (DSC)/Lagrange-distributed approximation function (LDAF) method is inferior to high order finite differences Free vibration analysis of symmetric laminated skew plates by discrete singular convolution technique based on first order shear deformation theory Discrete singular convolution-finite subdomain method for the solution of incompressible viscous flows Nonlinear dynamic response of laminated plates resting on nonlinear elastic foundations by the discrete singular convolution-differential quadrature coupled approaches Nonlinear analysis of thin rectangular plates on Winkler-Pasternak elastic foundations by DSC HDQ methods Differential quadrature Trefftz method for Poisson-type problems on irregular domains Differential quadrature Trefftz method for irregular plate problems Differential quadrature method based on the highest derivative and its applications Mesh Free Methods. Moving Beyond the Finite Element Method F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

64 Bibliography Meshless Methods and their Numerical Properties Classification and overview of meshfree methods On the random differential quadrature (RDQ) method: consistency analysis and application in elasticity problems On the convergence of random differential quadrature (RDQ) method and its application in solving nonlinear differential equations in mechanics Analysis of microelectromechanical systems using the meshless random differential quadrature method On the development of adaptive random differential quadrature method with an error recovery technique and its application in the locally high gradient problems Development of a novel strong-form meshless technique : random differential quadrature (RDQ) method with applications for 2-D multiphysics simulation of ph-sensitive hydrogel On the location of zeroes of polynomials from the stability analysis of novel strong-form meshless random differential quadrature method 2D simulation of the deformation of ph-sensitive hydrogel by novel strong-form meshless random differential quadrature method A random integral quadrature method for numerical analysis of the second kind of Volterra integral equations Laminated Composite Doubly-Curved Shell Structures

65 Bibliography Reproducing Kernel Particle Methods Reproducing Kernel Particle Methods for Structural Dynamics A new discretization method and its application to solve incompressible Navier-Stokes equations Domain-free discretization method for doubly connected domain and its application to simulate natural convection in eccentric annuli Radial basis function-enhanced domainfree discretization method and its applications Simulation of self-propelled anguilliform swimming by local domain-free discretization method Elasticity solution for free vibration of laminated beams State-Space-Based Differential Quadrature Method and Its Applications Free vibration of generally supported rectangular Kirchhoff plates: State-space-based differential quadrature method A hybrid elasticity method for bending and free vibration of composite laminates Free vibration of a functionally graded piezoelectric beam via statespace based differential quadrature F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

66 Bibliography Free vibration analysis of functionally graded annular plates by state-space based differential quadrature method and comparative modeling by ANN A state space differential reproducing kernel method for the 3D analysis of FGM sandwich circular hollow cylinders with combinations of simplysupported and clamped edges A hybrid moving least squares and differential quadrature (MLSDQ) meshfree method Moving least squares differential quadrature method and its application to the analysis of shear deformable plates Bending and buckling of thick symmetric rectangular laminates using the moving least-squares differential quadrature method Vibration analysis of symmetrically laminated plates based on FSDT using the moving least squares differential quadrature method Analysis of general shaped thin plates by the moving least-square differential quadrature method Moving least-squares differential quadrature method for free vibration of antisymmetric laminates Bending and buckling analysis of antisymmetric laminates using the moving least square differential quadrature method Laminated Composite Doubly-Curved Shell Structures

67 Bibliography Vibration analysis of generally laminated composite plates by the moving least squares differential quadrature method Dynamic stability analysis of FGM plates by the moving least squares differential quadrature method Physical decomposition of thin plate bending problems and their solution by mesh-free methods Coupling effects in elastic analysis of FGM composite plates by mesh-free methods Analysis of Beams with Transversal Gradations of the Young's Modulus and Variable Depths by the Meshless Method Analysis of composite plates using moving least squares differential quadrature method Element-free Galerkin methods Element-free Galerkin methods for static and dynamic fracture Crack propagation by element-free Galerkin methods Meshless methods: an overview and recent developments Element-free Galerkin method: convergence F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

68 Bibliography An adaptive approach with the element-free- Galerkin method A Modified collocation & penalty formulation for enforcing the essential boundary conditions in the Element Free Galerkin method A new Meshless Local Petrov-Galerkin (MLPG) approach to nonlinear problems in computer modeling & simulation A new Meshless Local Petrov-Galerkin (MLPG) approach in computational mechanics A critical assessment of the truly Meshless Local Petrov Galerkin (MLPG) and Local Boundary Integral Equation (LBIE) methods Analysis of thin beams using the Meshless Local Petrov-Galerkin method with Generalized Moving Least Squares Interpolations New concepts in meshless methods The meshless local Petrov-Galerkin (MLPG) approach for solving problems in elasto-statics Arbitrary placement of secondary nodes, and error control, in the meshless local Petrov-Galerkin (MLPG) method Meshless local Petrov-Galerkin (MLPG) method for convection-diffusion The Meshless Local Petrov-Galerkin (MLPG) method for solving incompressible Navier-Stokes equations A meshless local Petrov-Galerkin method for solving the bending problem of a thin plate Laminated Composite Doubly-Curved Shell Structures

69 Bibliography The meshless local Petrov-Galerkin (MLPG) method: A simple & less-costly alternative to the finite element and boundary element methods Meshless Local Petrov-Galerkin (MLPG) formulation for analysis of thick plates The Basis of meshless domain discretization: the meshless local Petrov-Galerkin (MLPG) method Applications of the MLPG Method in Engineering & Sciences: A Review A meshless Local Boundary Integral Equation (LBIE) method for solving nonlinear problems A Local Boundary Integral Equation (LBIE) method in computational mechanics, and a meshless discretization approach A Meshless Numerical Method Based on The Local Boundary Integral Equation (LBIE) to solve linear and nonlinear boundary value problems The local boundary integral equation (LBIE) and it's meshless implementation for linear elasticity Local boundary integral equation (LBIE) method for solving problems of elasticity with nonhomogeneous material properties Numerical integration of singularities in meshless implementation of local boundary integral equations A pure contour formulation for the meshless local boundary integral equation method in thermoelasticity F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

70 Bibliography Triangular mesh methods for the neutron transport equation On a finite element method for solving the neutron transport equation. In Mathematical Aspects of Finite Elements in Partial Differential Equations On discontinuous Galerkin methods Spline-based differential quadrature for fourth order differential equations and its application to Kirchhoff plates Non-linear vibration analysis of beams by a spline-based differential quadrature method Vibration analysis of rectangular plates with free corners using spline-based differential quadrature Solution of nonlinear initial-value problems by the splinebased differential quadrature method Symbolic computing in spline-based differential quadrature method Methods based on the differential quadrature in vibration analysis of plates Quartic B-spline differential quadrature method Numerical approach for solving diffusion problems using cubic B-spline collocation method Modified spline-based differential quadrature method applied to vibration analysis of truncated conical shells Laminated Composite Doubly-Curved Shell Structures

71 Bibliography Determination of the weighting coefficients for differential quadrature method based on spline interpolation Numerical solution of Burgers equation with modified cubic B-spline differential quadrature method Numerical Simulations of Boundary-Forced RLW Equation with Cubic B-Spline-based Differential Quadrature Methods Numerical solution of a uniform beam problem using g-spline-based differential quadrature method A general spline differential quadrature method based on quasi-interpolation Adaptive Computational Methods for Partial Differential Equations Accuracy Estimates and Adaptive Refinements in Finite Element Computations An expert system for the optimal mesh design in the hpversion of the finite element method Adaptive methods for Partial Differential Equations Toward a universal h-p adaptive finie element strategy, part 3, design of h-p meshes Finite Element Analysis F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

72 Bibliography, Applied Numerical Mathematics Modeling Mesh Generation and Adaptive Numerical Methods for Partial Differential Equations A Review of Posteriori Error Estimation and Adaptive Mesh Refinement Techniques Applied Numerical Mathematics Grid Generation and Adaptive Algorithms P- and Hp- Finite Element Methods: Theory and Applications in Solid and Fluid Mechanics (Numerical Mathematics and Scientific Computation) Differential quadrature method in the buckling analysis of beams and composite plates Differential quadrature for buckling analysis of laminated plates Generalized differential quadrature method for buckling analysis Application of differential quadrature method to the delamination buckling of composite plates Delamination buckling analysis of general laminated composite beams by differential quadrature method Application of the generalized differential quadrature method to deflection and buckling analysis of structural components Laminated Composite Doubly-Curved Shell Structures

73 Bibliography Vibration and Buckling Analyses of Beams by the Modified Differential Quadrature Method Differential quadrature buckling analyses of rectangular plates subjected to non-uniform distributed in-plane loadings Accurate buckling loads of thin rectangular plates under parabolic edge compressions by the differential quadrature method Buckling analysis of stiffened circular cylindrical panels using differential quadrature element method Differential quadrature analysis of the buckling of thin rectangular plates with cosine-distributed compressive loads on two opposite sides Buckling and post-buckling analysis of extensible beam columns by using the differential quadrature method Elastoplastic buckling analysis of thick rectangular plates by using the differential quadrature method Buckling analysis of functionally graded arbitrary straight-sided quadrilateral plates on elastic foundations Postbuckling analysis of variable angle tow plates using differential quadrature method Nonlinear bending analysis of thin circular plates by differential quadrature Application of the quadrature method to flexural vibration analysis of a geometrically nonlinear beam F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

74 Bibliography Deflection of plates with nonlinear boundary supports using generalized differential quadrature Numerical solution for differential equations of Duffing-type non-linearity using the generalized differential quadrature rule DQFEM analyses of static and dynamic nonlinear elastic-plastic problems using a GSR-based accelerated constant stiffness equilibrium iteration technique Nonlinear Vibration Analysis of Timoshenko Beams Using thedifferential Quadrature Method One-dimensional nonlinear consolidation of multi-layered soil by differential quadrature method Differential quadrature method for nonlinear vibration of orthotropic plates with finite deformation and transverse shear effect A differential quadrature nonlinear free vibration analysis of laminated composite skew thin plates Nonlinear transient dynamic response of clamped rectangular plates on two-parameter foundations by the algorithm of the singular convolution An assessment of the differential quadrature time integration scheme for nonlinear dynamic equations A differential quadrature algorithm for simulations of nonlinear Schrödinger equation Differential quadrature large amplitude free vibration analysis of laminated skew plates based on FSDT Laminated Composite Doubly-Curved Shell Structures

75 Bibliography An assessment of the differential quadrature time integration scheme for nonlinear dynamic equations Differential-algebraic approach to large deformation analysis of frame structures subjected to dynamic loads Nonlinear dynamics of axially accelerating viscoelastic beams based on differential quadrature Quadrature-difference methods for solving linear and nonlinear singular integro-differential equations Differential quadrature method for analyzing nonlinear dynamic characteristics of viscoelastic plates with shear effects Drillstring vibration analysis using differential quadrature method A semi-analytical method for nonlinear vibration of Euler-Bernoulli beams with general boundary conditions, Polynomial based differential quadrature method for numerical solution of nonlinear Burgers' equation A numerical solution of nonlinear parabolic-type Volterra partial integro-differential equations using radial basis functions Differential quadrature solution of nonlinear Klein Gordon and sine-gordon equations Size-dependent pull-in instability of hydrostatically and electrostatically actuated circular microplates F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

76 Bibliography A numerical scheme based on weighted average differential quadrature method for the numerical solution of Burgers equation Analysis of non-linear consolidation of soft clay by differential quadrature method Nonlinear free Vibrations of curved double walled carbon Nanotubes using differential quadrature method The differential quadrature solution of reaction-diffusion equation using explicit and implicit numerical schemes Error analysis in differential quadrature method Application of generalized differential quadrature method to structural problems Application of generalized differential quadrature to vibration analysis A comparative study of differential quadrature and cubature methods vis-à-vis some conventional techniques in context of convection-diffusionreaction problems A MATLAB differentiation matrix suite A variable order approach to improve differential quadrature accuracy in dynamic analysis Differential quadrature domain decomposition method for a class of parabolic equations Laminated Composite Doubly-Curved Shell Structures

77 Bibliography Isogeometric analysis of structural vibrations An isogeometric analysis approach for the study of structural vibrations Isogeometric Analysis. Toward Integration of CAD and FEA Comparison of generalized differential quadrature and Galerkin methods for the analysis of micro-electro-mechanical coupled systems Boundary reduction technique and triangular differential quadrature domain decomposition method for polygonal region A mixed modal-differential quadrature method for free and forced vibration of beams in contact with fluid New Insights into the Strong Formulation Finite Element Method for Solving Elastostatic and Elastodynamic Problems A Strong Formulation Finite Element Method (SFEM) Based on RBF and GDQ Techniques for the Static and Dynamic Analyses of Laminated Plates of Arbitrary Shape The Strong Formulation Finite Element Method: Stability and Accuracy Free Vibrations of Free-Form Doubly- Curved Shells Made of Functionally Graded Materials Using Higher-Order Equivalent Single Layer Theories An Accurate One- Dimensional Theory for the Dynamics of Laminated Composite Curved Beams F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

78 Bibliography Accurate Inter-Laminar Recovery for Plates and Doubly-Curved Shells with Variable Radii of Curvature Using Layer-Wise Theories Strong Formulation Finite Element Method Based on Differential Quadrature: A Survey Stress and Strain Recovery for Functionally Graded Free-Form and Doubly-Curved Sandwich Shells Using Higher- Order Equivalent Single Layer Theory Vibration Analysis of Multi- Stepped and Multi-Damaged Parabolic Arches Using GDQ Stress and Strain Recovery of Laminated Composite Doubly-Curved Shells and Panels Using Higher-Order Formulations Refined 2D and Exact 3D Shell Models for the Free Vibration Analysis of Single- and Double-Walled Carbon Nanotubes Radial Basis Functions Based on Differential Quadrature Method for the Free Vibration of Laminated Composite Arbitrary Shaped Plates Numerical and Exact Models for Free Vibration Analysis of Cylindrical and Spherical Shell Panels Dynamic Analysis of Thick and Thin Elliptic Shell Structures Made of Laminated Composite Materials Free Vibrations of Composite Oval and Elliptic Cylinders by the Generalized Differential Quadrature Method Laminated Composite Doubly-Curved Shell Structures

79 Bibliography A New Approach for Treating Concentrated Loads in Doubly-Curved Composite Deep Shells with Variable Radii of Curvature Higher-Order Theories for the Free Vibration of Doubly-Curved Laminated Panels with Curvilinear Reinforcing Fibers by Means of a Local Version of the GDQ Method Vibration Analysis of Variable Thickness Plates and Shells by the Generalized Differential Quadrature Method 3D Exact and 2D Generalized Differential Quadrature Models for Free Vibration Analysis of Functionally Graded Plates and Cylinders A SFEM-Based Evaluation of Mode-I Stress Intensity Factor in Composite Structures Four-Parameter Functionally Graded Cracked Plates of Arbitrary Shape: a GDQFEM Solution for Free Vibrations Free Vibration Analysis of Conical Shells Reinforced with Agglomerated Carbon Nanotubes General Higher Order Layer-Wise Theory for Free Vibrations of Doubly-Curved Laminated Composite Shells and Panels Higher-Order Structural Theories for the Static Analysis of Doubly-Curved Laminated Composite Panels Reinforced by Curvilinear Fibers The Local GDQ Method for the Natural Frequencies of Doubly-Curved Shells with Variable Thickness: A General Formulation Effect of Agglomeration on the Natural Frequencies of Functionally Graded Carbon Nanotube-Reinforced F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

80 Bibliography Laminated Composite Doubly-Curved Shells Inter-Laminar Stress Recovery Procedure for Doubly-Curved, Singly-Curved, Revolution Shells with Variable Radii of Curvature and Plates Using Generalized Higher-Order Theories and the Local GDQ Method Generalized Stress-Strain Recovery Formulation Applied to Functionally Graded Spherical Shells and Panels Under Static Loading Vibration Problems in Engineering Strength of Materials A Treatise on the Mathematical Theory of Elasticity Tensor Analysis, Theory and Applications Theory of Elasticity Mathematical Theory of Elasticity The stress analysis of pressure vessels and pressure vessel components Elasticity: Theory and Applications Theory of Elasticity of an Anisotropic Body Theory of Elasticity Stresses in Aircraft and Shell Structures An Improved First Approximation Theory of Thin Shells Theory of Plates and Shells Stresses in Shells Theory of Elastic Thin Shells Thin Shell Theory Laminated Composite Doubly-Curved Shell Structures

81 Bibliography Theory of Anisotropic Shells General Theory of Shells and Its Applications in Engineering Thin Elastic Shells Anisotropic Plates Vibration of Plates Flutter, Vibration and Buckling of Truncated Orthotropic Conical Shells with Generalized Elastic Edge Restraint The Stress Analysis of Pressure Vessel and Pressure Vessel Components Vibration of Shells Theory and Analysis of Plates Aeroelasticity of Plates and Shells Beams, Plates and Shells The Dynamics of Arches and Frames Theory of Shell Structures Finite Element Analysis of Shells of Revolution Shell Theory The Mechanics of Vibrations of Cylindrical Shells A Theory of Latticed Plates and Shells Piezoelectric Shells The Behavior of Shells Composed of Isotropic and Composite Materials The Theory of Piezoelectric Shells and Plates Structural Vibration: Analysis and Damping Mechanics of Composite Materials The Nonlinear Theory of Elastic Shells F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

82 Bibliography Vibration of Mindlin Plates Analysis of Shells and Plates Continuum Mechanics for Engineers Mechanics of Composite Materials Theory and Analysis of Elastic Plates Nonlinear Theory of Shallow Shells Theory of Shells Shear Deformable Beams and Plates Mechanics and Analysis of Composite Materials Thin Plates and Shells Asymptotic Methods in the Buckling Theory of Elastic Shells Energy Principles and Variational Methods in Applied Mechanics The Behaviour of Structures Composed of Composite Materials Composite Materials, Design and Applications Mechanics of Laminated Composite Plates and Shells Mechanics of Solids and Shells Buckling of Thin Metal Shells Mechanics of Elastic Composites Vibration of Laminated Shells and Plates Vibrations of Shells and Plates Design of Plate and Shell Structures Rotating Shell Dynamics Laminated Composite Doubly-Curved Shell Structures

83 Bibliography Exact Solutions for Buckling of Structural Members An Introduction to the Mathematical Theory of Vibrations of Elastic Plates Thermo-Dynamics of Plates and Shells Nonlinear Vibrations and Stability of Shells and Plates Elasto-Plastic and Damage Analysis of Plates and Shells Vibration of Plates Composite Materials, Science and Applications Plates and Shells for Smart Structures: Classical and advanced theories for modeling and analysis The Finite Element Analysis of Shells - Fundamentals Vibrations of Continuous Systems Theory and design of plate and shell structures Advanced Mechanics of Composite Materials and Structural Elements Shell Structures for Architecture. Form Finding and Optimization Strutture a Guscio in Materiale Composito I. Geometria Differenziale. Teorie di Ordine Superiore Strutture a Guscio in Materiale Composito II. Quadratura Differenziale e Integrale. Elementi Finiti in Forma Forte F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

84 Bibliography Structural Vibration A Uniform Accurate Solution for Laminated Beams, Plates and Shells with General Boundary Conditions The effect of transverse shear deformation on the bending of elastic plates Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates Solution of Vandermonde systems of equations Elastic deformation of thick, laminated composite shells Accurate theory for laminated composite deep thick shells General equations of anisotropic plates and shells including transverse shear deformations, rotary inertia and initial curvature effects Recent research advances in the dynamic behavior of shells: , Part 1: laminated composite shells Recent research advances in the dynamic behavior of shells: , Part 2: homogeneous shells Free vibration of non-uniform composite cylindrical shells Recent research advances on the dynamics analysis of composite shells: A higher-order shell model applied to shells with mixed boundary conditions Review of Recent Literature on Static Analyses of Composite Shells: Laminated Composite Doubly-Curved Shell Structures

85 Bibliography Free vibration, buckling, and static deflection of functionally graded plates Large deformation analysis of functionally graded shells Linear thermoelastic buckling and free vibration behaviour of functionally graded truncated conical shells Natural frequencies of functionally graded plates by a meshless method Buckling and free vibration analysis of functionally graded cylindrical shells subjected a temperature-specified boundary condition Active control of FGM plates with integrated piezoelectric sensors and actuators Finite element method for the feedback control of FGM shells in the frequency domain via piezoelectric sensors and actuators An analytical solution for nonlinear cylindrical bending of functionally graded plates Dynamic stability analysis of functionally graded cylindrical shells under periodic axial loading Free vibration analysis of functionally graded elliptical cylindrical shells using higher-order theory F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

86 Bibliography An exact solution for the steady-state thermoelastic response of functionally graded orthotropic cylindrical shells Vibration suppression of FGM shells using embedded magnetostrictive layers Supersonic flutter characteristics of functionally graded flat panels including thermal effect Finite element analysis of smart functionally graded plates A radial basis function for the free vibration analysis of functionally graded plates using refined theory Postbuckling analysis of pressure-loaded functionally graded cylindrical shells in thermal environments Functionally Graded Materials, Nonlinear Analysis of Plates and Shells The stability of functionally graded truncated conical shells subjected to aperiodic impulsive loading The stability of compositionally graded ceramic-metal cylindrical shells under aperiodic axial impulsive loading Thermoelastic stability of functionally graded truncated conical shells Nonlinear analysis of functionally graded plates and shallow shells Thermomechanical postbuckling analysis of moderately thick functionally graded plates and shallow shells Free vibration and parametric resonance of shear deformable functionally graded cylindrical panels Laminated Composite Doubly-Curved Shell Structures

87 Bibliography Generalized shear deformation theory for bending analysis of functionally graded plates Dynamic equilibrium equations of composite anisotropic beams considering the effects of transverse shear deformations and structural damping Problems encountered from the use (or misuse) of Rayleigh damping Dynamic analysis for three-dimensional laminated plates and panels with damping Analisi Vettoriale Differential Geometry of Curves and Surfaces Geometria Differenziale Curves and Surfaces for Computer Aided Geometric Design Geometry of Surfaces The NURBS Book Differential Geometry and Its Applications Lezioni di Geometria Differenziale. Curve e Superfici Differential Geometry, Curves, Surfaces, Manifolds Modern Differential Geometry of Curves and Surfaces with Mathematica Differential Geometry: Theory and Applications Isogeometric Analysis. Toward Integration of CAD and FEA Elementary Differential Geometry F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

88 Bibliography Scienza delle costruzionivol. 1 Scienza delle costruzioni. Vol. 2 Scienza delle costruzionivol Scienza delle costruzioni. Vol. 4 Esercizi di Algebra Lineare e Geometria Analisi Numerica Fondamenti di Calcolo Numerico The Finite Element Method Algebra Lineare e Geometria Calcolo Automatico delle Strutture Calcolo Matriciale delle Strutture 1-2 Handbook of Computational Methods for Integration Gradiente Rotore Divergenza Isogeometric Analysis. Toward Integration of CAD and FEA MATLAB Codes for Finite Element Analysis Progettare i Gusci Beam Structures. Classical and Advanced Theories Esercizi di Meccanica delle Strutture. I materiali compositi Esercitazioni di Scienza delle Costruzioni 1. Strutture Isostatiche e Geometria delle Masse Esercitazioni di Scienza delle Costruzioni 2. Strutture Iperstatiche e Verifiche di Resistenza Esercitazioni di Scienza delle Costruzioni 3. Introduzione all Analisi Probabilistica delle Strutture Esercitazioni di Scienza delle Costruzioni 4. Temi d Esame Scienza delle Costruzioni. Teoria dell Elasticità Laminated Composite Doubly-Curved Shell Structures

89 Bibliography Scienza delle Costruzioni. Teoria della Trave Fondamenti di Analisi Matriciale delle Strutture Fondamenti di Dinamica e Vibrazione delle Strutture. Sistemi Discreti Fondamenti di Dinamica e Vibrazione delle Strutture. Sistemi Continui Lezioni di Scienza delle Costruzioni Teoria delle Strutture. Stati tensionali e piastre Teoria delle Strutture. Gusci di rivoluzione Comportamento Dinamico dei Gusci Cilindrici: Formulazione e Soluzione Sul Comportamento delle Volte Cilindriche Effetto della Curvatura sulla Risposta dei Gusci in Materiale Anisotropo Teorie di Ordine Superiore per Strutture a Doppia Curvatura in Materiale Anisotropo DiQuMASPAB Software F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

90