Laminated Composite Doubly-Curved Shell Structures

Transcription

1

2 Francesco Tornabene Nicholas Fantuzzi Michele Bacciocchi Erasmo Viola Laminated Composite Doubly-Curved Shell Structures Differential Geometry Higher-Order Structural Theories Volume I

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 Classification based on shape Classification based on the curvature Classification based on the developability Laminated Composite Doubly-Curved Shell Structures

11 Index F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

12 Index Anisotropic materials Material symmetry Monoclinic materials Orthotropic materials Transversely isotropic materials Isotropic materials Laminated Composite Doubly-Curved Shell Structures

13 Index Fibrous composites: unidirectional lamina Granular composites: Functionally Graded Materials Functionally Graded Carbon Nanotube-reinforced composites Variable Angle Tow composites Composite laminates Symmetric laminates Antisymmetric laminates Balanced and almost-isotropic laminates External actions on the bottom and top shell surfaces Volume forces Seismic excitation Shell resting on elastic foundation F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

14 Index External actions on the bottom and top shell surfaces Volume forces Seismic excitation Shell resting on elastic foundation Laminated Composite Doubly-Curved Shell Structures

15 Index F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

16 Index Composites made of a single lamina Symmetric laminates Antisymmetric laminates Balanced and almost isotropic laminates Kinematic equations Constitutive equations Indefinite equilibrium equations Fundamental equations Laminated Composite Doubly-Curved Shell Structures

17 Index Conical shell Circular cylindrical shell Circular plate Rectangular plate Conical membrane Circular cylindrical membrane F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

18 Index Circular membrane Rectangular membrane Laminated Composite Doubly-Curved Shell Structures

19 Index F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

20 Preface Laminated Composite Doubly-Curved Shell Structures Differential Quadrature Differential Geometry 3D ElasticityEquivalent Single Layer Layer-Wise 3D Elasticity Equations in Principal Curvilinear Coordinates Laminated Composite Doubly-Curved Shell Structures

21 Preface Higher-order Shear Deformation Theories Carrera Unified Formulation F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

22 Preface Functionally Graded Materials structural damping Rayleigh proportional damping Laminated Composite Doubly-Curved Shell Structures

23 Preface surface forcesvolume forces Classical Shell Theories First-order Shear Deformation Theories Higher-order Shear Deformation Theories thin shells arches beamstheory of Composite Thin Shells Kirchhoff-Love Theory Membrane Theory Theory of Composite Arches and Beams Timoshenko TheoryEuler-Bernoulli Theory F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

24 Preface Engineering Theories Doubly- and Singly-Curved shells, degenerate shells Plane Beams with Curvilinear and Straight Axes Laminated Composite Doubly-Curved Shell Structures

25 Preface The book is aimed primarily at graduate students at the intermediate level in engineering mechanics, aerospace engineering, mechanical engineering and civil engineering, whose field of specialization is solid mechanics. Stress analysts in industry will find the book a useful introduction that will equip them to read further in the literature of solutions to technically important shell problems, while research specialists will find it useful as an introduction to current theoretical work. This volume is not intended to be an exhaustive treatise on the theory of thinelastic shells but, rather, a broad introduction from which each reader can follow his own interests further 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 F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

26 Preface Center of Study and Research for the Identification of Materials and Structures Laminated Composite Doubly-Curved Shell Structures

27

28 Bibliography A Differential Quadrature Method Solution for Shear-Deformable Shells of Revolution Static Analysis of Shear-Deformable Shells via G.D.Q. Method The G.D.Q. Method for the Harmonic Dynamic Analysis of Rotational Shell Structural Elements Analytical and Differential Quadrature Results for Vibration Analysis of Damaged Circular Arches Vibration analysis of damaged circular arches with varying cross-section Free Vibration Analysis of Spherical Caps using G.D.Q. Numerical Solution Vibration analysis of conical shell structures using GDQ Method 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 Laminated Composite Doubly-Curved Shell Structures

29 Bibliography Dynamical analysis of spherical shell structural elements using the First Order Shear Deformation TheoryMechanical Vibration: where do we stand? Nonconservative stability problems via Generalized Differential Quadrature Method 2-D solution for free vibrations of parabolic shells using Generalized Differential Quadrature Method 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 2-D Differential Quadrature solution for vibration analysis of functionally graded conical, cylindrical and annular shell structures Free vibrations of three parameter functionally graded parabolic panels of revolution Critical flow speeds of pipes conveying fluid by the Generalized Differential Quadrature Method F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

30 Bibliography 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 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 Laminated Composite Doubly-Curved Shell Structures

31 Bibliography 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 Radial basis function method applied to doubly-curved laminated composite shells and panels with a general higher-order equivalent single layer theory 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 General higher-order equivalent single layer theory for free vibrations of doubly-curved laminated composite shells and panels Generalized differential quadrature finite element method for cracked composite structures of arbitrary shape 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 Soft core plane state structures under static loads using GDQFEM and Cell Method F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

32 Bibliography GDQFEM numerical simulations of continuous media with cracks and discontinuities On Static Analysis of Plane State Structures via GDQFEM and Cell Method New Insights into the Strong Formulation Finite Element Method for Solving Elastostatic and Elastodynamic Problems 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 Generalized Differential Quadrature Finite Element Method for Vibration Analysis of Arbitrarily Shaped Membranes 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 Analysis of thick isotropic and cross-ply laminated plates by generalized differential quadrature method and a unified formulation The Local GDQ Method Applied to General Higher-Order Theories of Doubly-Curved Laminated Composite Shells and Panels: the Free Vibration Analysis The Strong Formulation Finite Element Method: Stability and Accuracy Laminated Composite Doubly-Curved Shell Structures

33 Bibliography Free Vibrations of Free-Form Doubly- Curved Shells Made of Functionally Graded Materials Using Higher-Order Equivalent Single Layer Theories Static analysis of doubly-curved anisotropic shells and panels using CUF approach, differential geometry and differential quadrature method 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 Refined 2D and Exact 3D Shell Models for the Free Vibration Analysis of Single- and Double-Walled Carbon Nanotubes An Accurate One- Dimensional Theory for the Dynamics of Laminated Composite Curved Beams 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 F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

34 Bibliography Free Vibrations of Composite Oval and Elliptic Cylinders by the Generalized Differential Quadrature Method Accurate Inter-Laminar Recovery for Plates and Doubly-Curved Shells with Variable Radii of Curvature Using Layer-Wise Theories 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 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 Vibration Analysis of Variable Thickness Plates and Shells by the Generalized Differential Quadrature Method Laminated Composite Doubly-Curved Shell Structures

35 Bibliography 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 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 F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

36 Bibliography 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 Theory of Anisotropic Shells General Theory of Shells and Its Applications in Engineering Thin Elastic Shells Anisotropic Plates Vibration of Plates Laminated Composite Doubly-Curved Shell Structures

37 Bibliography 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 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 F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

38 Bibliography 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 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 Laminated Composite Doubly-Curved Shell Structures

39 Bibliography Elasto-Plastic and Damage Analysis of Plates and Shells Vibration of Plates Composite Materials, Science and Applications Progettare i Gusci 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 Meccanica delle Strutture a Guscio in Materiale Composito. Il metodo Generalizzato di Quadratura Differenziale Theory and design of plate and shell structures Advanced Mechanics of Composite Materials and Structural Elements Mechanics of Laminated Composite Doubly-Curved Shell Structures. The Generalized Differential Quadrature Method and the Strong Formulation Finite Element Method 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 Structural Vibration A Uniform Accurate Solution for Laminated Beams, Plates and Shells with General Boundary Conditions F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

40 Bibliography 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: Free vibration, buckling, and static deflection of functionally graded plates Laminated Composite Doubly-Curved Shell Structures

41 Bibliography 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 An exact solution for the steady-state thermoelastic response of functionally graded orthotropic cylindrical shells Vibration suppression of FGM shells using embedded magnetostrictive layers F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

42 Bibliography 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 Generalized shear deformation theory for bending analysis of functionally graded plates Laminated Composite Doubly-Curved Shell Structures

43 Bibliography 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 Scienza delle costruzionivol. 1 Scienza delle costruzioni. Vol. 2 Scienza delle costruzionivol F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

44 Bibliography 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 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 Scienza delle Costruzioni. Teoria della Trave Fondamenti di Analisi Matriciale delle Strutture Fondamenti di Dinamica e Vibrazione delle Strutture. Sistemi Discreti Laminated Composite Doubly-Curved Shell Structures

45 Bibliography 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 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 F. Tornabene, N. Fantuzzi, M. Bacciocchi, E. Viola

46 Bibliography Guided Waves in Structures for SHM. The Time-Domain Spectral Element Method 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 Comportamento Dinamico dei Gusci Cilindrici: Formulazione e Soluzione Sul Comportamento delle Volte Cilindriche Modellazione e Soluzione di Strutture a Guscio in Materiale Anisotropo Effetto della Curvatura sulla Risposta dei Gusci in Materiale Anisotropo Generalized Differential Quadrature Finite Element Method applied to Advanced Structural Mechanics Teorie di Ordine Superiore per Strutture a Doppia Curvatura in Materiale Anisotropo DiQuMASPAB Software Laminated Composite Doubly-Curved Shell Structures

47

48