COROTATIONAL NONLINEAR DYNAMIC ANALYSIS OF LAMINATED COMPOSITE SHELL STRUCTURES
|
|
- Jonathan Montgomery
- 6 years ago
- Views:
Transcription
1 Copyright c 009 by ABCM January 04-08, 010, Foz do Iguaçu, PR, Brazil COROTATIONAL NONLINEAR DYNAMIC ANALYSIS OF LAMINATED COMPOSITE SHELL STRUCTURES Felipe Schaedler de Almeida, schaedleralmeida@gmail.com Armando Miguel Awruch, amawruch@ufrgs.br Graduate Program in Civil Engineering, Federal University of Rio Grande do Sul, Av. Osvaldo Aranha, 99, Porto Alegre, RS, Brazil Abstract. The dynamic analysis of laminated composite shell structures is performed using a simple displacementbased 18-degree-of-freedom triangular flat shell element, obtained by the superposition of a membrane element and a plate element. The membrane element is based on the assumed natural deviatoric strain formulation (ANDES), having corner drilling degrees of freedom and optimal in-plane bending response. The plate element employs the Timoshenko s laminated composite beam function to define the deflections and rotations on the element boundaries. This formulation provides first-order shear flexibility to the element and naturally avoids shear-locking problems as thin shells are analyzed. The geometrically nonlinear behavior of the structures is achieved by the element independent corotational formulation (EICR) together with a consistent treatment of finite rotations. An energy conserving procedure for the time-integration of the nonlinear dynamic equations is also included. Finally, two examples are presented to show that the algorithm is able to solve highly nonlinear dynamic problems. Keywords: Laminated composite materials, Shell structures, Nonlinear dynamics 1. INTRODUCTION Laminated composites as structural materials has becoming a very important aspect in structural design. This is reflected in the growing amount of researches devoted to this subject. One of the main interesting research fields for the engineering community is those related to the computational modeling and analysis of laminated composite structures. Correct prediction of the mechanical behavior is an essential condition for the introduction of laminated composites in critical structural applications. Laminates are very attractive due to their high mechanical performance and to the possibility of tailoring their properties to specific application by adjustments of fiber orientation and stacking sequence. Considerable modifications on the plate or shell stiffness can be obtained by the adoption of different lamination sequences, as will be shown latter. Furthermore, the ply ortotropicity leads the laminate mechanical behavior to be more complex than for isotropic materials, with the rising of coupling deformation modes and high shear deformation sensitivity. Together to the uncommon material behavior, other sophistications may also be considered in computational analysis in order to correctly determine the response of laminated composite structures. Geometric nonlinearity is one of the aspects to be taken into account for the analysis improvement, since large displacements and rotations may be observed in many structural application. Dynamics is other point frequently present in structural designs and must be carefully studied to provide realistic predictions. This work aims to present a numerical study on the dynamic analyses of laminated composite shells considering geometrically nonlinear effects. The algorithm employed for the analysis is composed by a linear composite shell element associated with the element independent corotational formulation (EICR) (Nour-Omid and Rankin, 1991), to account for the geometric nonlinearity with finite rotations, and the approximately energy-conserving corotational procedure (AECCP) (Crisfield, 1997) to perform the dynamic analysis. Theoretical aspects are briefly discussed in the next section, followed by a section with numerical studies on the nonlinear dynamic analysis of shells.. COROTATIONAL NONLINEAR DYNAMIC ANALYSIS OF SHELLS The construction of the present algorithm is achieved by first implementing a shell element for the linear static analysis and subsequently applying the approximately energy-conserving corotational procedure (AECCP), based on the element independent corotational formulation (EICR), to expand the element capabilities to the nonlinear dynamic analysis of shells. A triangular flat shell element implemented based on static linear formulation is obtained by the superposition of threenoded membrane and plate elements, as shown in Fig. 1, resulting in a 18-dof element. The membrane element used in the composition of the shell element is given by Felippa (003). This element is based on the assumed natural deviatoric strain formulation (ANDES) and possesses two in-plane translations and one drilling rotation per node. Although the original formulation is developed to give optimal response for pure in-plane bending of isotropic membranes, the element application is expanded here for the analysis of laminated composite materials, following the recommendations given in
2 Proceedings of PACAM XI Copyright c 009 by ABCM January 04-08, 010, Foz do Iguaçu, PR, Brazil the above reference work. The plate element adopted to fill the bending and transverse shearing stiffness of the shell element is given by Zhang and Kim (005). This element takes into account laminated composite sections and first order shear flexibility by using the Timoshenko s laminated composite beam function to interpolate in-plane rotations and transverse displacements in the element sides. The absence of shear-locking problems is inherited by the plate element from the Timoshenko s laminated beam function, which provides a unified formulation for the analysis of thin and thick plates and shells without any stabilization scheme. Figure 1. Membrane + plate degrees of freedom = shell degrees of freedom The extension of the finite element for linear static analysis to the geometrically nonlinear analysis is obtained by the application of the EICR formulation (Nour-Omid and Rankin, 1991). Basically, the variation of local displacements δpl (in the element corotational system) is related to the variation of the global displacements δp by a transformation matrix Λ, as given in Eq.(1). As finite rotations are considered in the EICR formulation, the nodal rotations are defined by tensors R, represented by 3 3 matrices, while the rotation variations are defined by a spin vector ω (Felippa and Haugen, 005). The transformation matrix, given in Eq.(), is composed by three matrices: H which transform the spin vector ω (containing variations of the rotations) in the additive rotations (θx,θy and θz ), P which extract the deformation part of the rotations and displacements (ommiting rigid rotations and displacements) and T which transform the global variable into local variables. The formulation for the transformation matrices and the update of rotations are given in many reference works on corortational formulation as Felippa and Haugen (005), Crisfield (1997) and Nour-Omid and Rankin (1991). δpl = Λδp (1) Λ = HPT () Considering the linear relation between the local displacements pil and the local nodal forces qil given by the linear stiffness matrix Kl, and the local-global displacement transformation given in Eq.(1), it is possible to express the global nodal forces in terms of local displacements by the Eq.(3), which is derived by equating the virtual work in the local and in the global reference systems. The tangent stiffness matrix Kt is defined by the variation of the internal forces with respect to the global displacements, as given in Eq.(4) (Felippa and Haugen, 005), where Λt Kl Λ is called material stiffness matrix and Ktσ is called geometric stiffness matrix. qil = Λt qil = Λt Kl pil (3) δqi = Λt δqil + δλt qil = Λt Kl Λ + Ktσ (qil ) δp = Kt δp (4) The AECCP was developed by Crisfield (1997) as an approximation to the corotational mid-point dynamic algorithm (Crisfield and Shi, 1994), introduced in order to conserve the full energy of the mechanical system. Mid-point algorithms are constructed by equating the change of total momentum of the system to the impulse of internal and external forces acting on the system during the time step (Crisfield et al., 1997). The equilibrium equation is given by Eq.(5), where, K, P and φ are the kinetic, external and strain energy increments in the time step, respectivelly; qmass,m, qe,m and qi,m are the mid-point inertial, external and internal nodal element forces, respectively. The mid-point vectors form an equivalent force vector gm that may vanish as the numerical integration reaches convergence, conserving approximately the total energy of the system. t K + P + φ p = 0 (5) = qtmass,m qte,m + qti,m p = gm The mid-point inertial vector is defined for a specific element by Eq.(6), where t is the time increment, M is the element mass matrix and p is the nodal velocities vector, which contains both translational global velocities and, body
3 Copyright c 009 by ABCM January 04-08, 010, Foz do Iguaçu, PR, Brazil attached angular velocities. The relation between spatial and body attached angular velocities is given for the vector ṗ by R e,n+1, which is a block diagonal matrix defined in Eq.(7) (Crisfield et al., 1997). Following Crisfield et al. (1997), in this work the mass matrix is built direcly in the global reference system by interpolating global velocities. q mass,m = 1 t ( R e,n+1 Mṗ n+1 R e,nmṗ n ) (6) R e,n = diag [ I R 1,n I R,n I R 3,n ] (7) The external and internal forces acting on the structures between the time n and n+1 are represented by their mid-point values, given in Eq.(8) and Eq.(9), respectively. q e,m = q e,n+1 + q e,n (8) ( ) t Λn+1 + Λ n q i,n+1 + q i,n q i,m = Like for the static cortational formulation (Eq.(4)), an equivalent tangent stiffness matrix is obtained by the variation of the equivalent force vector g m with respect to the global displacements. The equivalent tangent stiffness matrix is formed by the inertial contribution, given in Eq.(10) and the static contribution, given in Eq.(11). No contribution to the equivalent stiffness is originated by the external forces as long as they are conservatives. The complete derivation of K mass are given in Crisfield (1997) for beam elements; however, as only terms related to nodes are varied, the same formulation can be applied for triangular shell elements with the addition of one node with respect to the beam element. δq mas,m = 1 t ( δr e,n+1 Mṗ n+1 + R e,n+1mδṗ n+1 ) = Kmas (10) (9) ( ) t ( ) t Λn+1 + Λ n δq i,n+1 δλn+1 q i,n+1 + q i,n δq i,m = + [ (Λn+1 ) t ( ) ] + Λ n K l = Λ qi,n+1 + q i,n n + K tσ δp (11) The procedure to integrate the equilibrium equations (Eq. (5)) in time is given by Crisfield (1997), where initially a predictor step is used, followed by corrector iterations. The predictor step is necessary since p n+1, ṗ n+1 and q i,n+1 are not known at the beginning of the integration in a new time step. 3. EXAMPLES In this section two examples of the solution of nonlinear dynamic problems are presented. 3.1 Nonlinear transient response of cylindrical composite shells The nonlinear transient analysis of three specially laminated composite shells are present in this example. The geometry of the simply supported spherical panel is presented in Fig. a, where R = 5m and a = 0.5m. Two values for the total thickness of the shell (h) are considered, being their values given by the geometrical relations a/h = 100 and a/h = 50. The laminates under consideration are a bending stiff laminate [0 / ± 30 ] s, a quasi-isotropic laminate [0 / ± 45 /90 ] s, and a torsion stiff laminate [±45 / 45 ] s. These laminates are made using the T300/508 CFRP (carbon fiber reinforced polymer) composite, with the following properties (Kundu and Sinha, 006): E 11 = 181 GPa, E = 10.3 GPa, G 1 = G 13 = 7.17 GPa, G 3 = 3.58 GPa, ν 1 = 0.8 and ρ = 1600 kg/m 3. All plies of each laminate have the same thickness. The structure is loaded by a suddenly applied step internal pressure of N/m. The normalized vertical displacement of the panel center (u z /h) obtained in this work using a mesh with rectangles with two triangles each one (corresponding to 51 elements and 89 nodes) to describe the whole shell and a time step increment t = s, are presented in Fig.b, Fig.c and Fig.d for the bending stiff, quasi-isotropic and torsion stiff laminates, respectively. The time increment and the number of nodes are equal to those adopted by Kundu and Sinha (006), which performed the analyses using a nine-noded isoparametric composite shell element considering first order shear deformation and developed in curvilinear coordinates. The reference work is based on the total lagrangian approach and the Newmark method has been used for the time integration.
4 Copyright c 009 by ABCM January 04-08, 010, Foz do Iguaçu, PR, Brazil Figure. Simply supported spherical shell: (a) Geometry (b) Response for the bending stiff laminate [0 / ± 30 ] s (c) Response for the quasi-isotropic laminate [0 / ± 45 /90 ] s (d) Response for the torsion stiff laminate [±45 / 45 ] s Results obtained by the present work compare very well with those given by the reference, as can be seen in Figures b-d. Only a tiny difference in the period and amplitude of the panel center vertical displacement is observed for the laminates with ratio a/h = 100. The ability of the present element in capture the change in stiffness due to different staking sequences is demonstrated in this example by the variety of laminates considered. 3. Motion of a short cylinder This is a classical example, first presented by Simo and Tarnow (1994), and widely used to demonstrate the ability of the proposed formulations in solving problems with large motion (displacements and rotations) for long-term computations. Due to the lack of reference examples dealing with dynamic large motion analysis of laminated composite structures in the literature, this example is adopted in the present work to demonstrate that the implemented algorithm also posses the mentioned characteristics, in spite of the fact that an isotropic material is considered. The geometry of the short cylinder is defined by the diameter D = 15, the height H = 3 and the thickness h = 0.0. The material characteristics are: Young s modulus E = 10 8, Poisson s ratio ν = 0.5 and mass density ρ = 1. The loading conditions applied for the nodes located in positions described by the angles 0, 90, 180 and 360 taken anticlockwise from the x axis are given in Fig.3, as well as the amplitude function f(t). Like in the reference work (Brank et al., 003), a mesh with 8 3 retangles with two triangles each one (corresponding to 168 triangular elements and 84 nodes) is used to model the shell. However, the maximum time step increment that lead to correct results for this work is t = s, which is half the time step used by Brank et al. (003), but.5 times bigger than the time step used by Simo and Tarnow (1994). The displacements of the point A, shown in Fig.3, initially located at ( D, 0, 0), are presented in Fig.4a, where the results obtained in this work are compared to those given by Brank et al. (003). Very good agreement is observed. Figure 4b, shows velocity results for the same point. As the response obtained in the reference work is quite noisy it could not be reproduced here, but the mean value of the velocities agree well with those obtained by the present work. The energy conservative property, inherent of the method adopted in the present work, is demonstrated in Fig. 4c, where the
5 Copyright c 009 by ABCM January 04-08, 010, Foz do Iguaçu, PR, Brazil Figure 3. Short cylinder geometry and load condition. kinetic energy (K) and strain potential energy (P) are plotted. Again, the results obtained here compare very well with those presented by Brank et al. (003). Finally, Fig. 4d illustrates the motion of the cylinder by depicting a sequence of deformed shapes, without any magnification of the actual deformations. Figure 4. Short cylinder: (a) Displacements of point A (b) Velocities of point A (c) Kinetic and strain potential energies (d) Sequence of deformed shapes 4. CONCLUSIONS The two examples demonstrated that the implemented algorithm is able to correctly perform nonlinear dynamic analysis of composite structures. In the first example three different laminates where studied, showing that the finite element is able to reproduce the change of stiffness due to specific stacking sequences in each laminte. The second example showed that problems with large displacements and rotations can aslo be solved by the algorithm. The stability of the method, based on the conservation of the total energy, was demonstrated in the second example by plotting kinetic and strain
6 Copyright c 009 by ABCM January 04-08, 010, Foz do Iguaçu, PR, Brazil energy. 5. ACKNOWLEDGEMENTS The authors wish to thank the Brazilian agencies CNPq and CAPES for their financial support. 6. REFERENCES Brank, B., Korelc, J., and Ibrahimbegovic, A Dynamics and time-stepping schemes for elastic shells undergoing finite rotations. Computers and Structures, Vol.81(1): Crisfield, M., Galvanetto, U., and Jelenic, G Dynamics of 3-d co-rotational beams. Computational Mechanics, Vol.0(6): Crisfield, M. and Shi, J Co-rotational element/time-integration strategy for non-linear dynamics. International Journal for Numerical Methods in Engineering, Vol.37(11): Crisfield, M. A Non-linear Finite Element Analysis of Solid and Structures - Vol: Advanced Topics. Wiley. Felippa, C. and Haugen, B A unified formulation of small-strain corotational finite elements: I. theory. Computer Methods in Applied Mechanics and Engineering, Vol.194(1-4): Felippa, C. A A study of optimal membrane triangles with drilling freedoms. Computer Methods in Applied Mechanics and Engineering, Vol.19(16-18): Kundu, C. and Sinha, P Nonlinear transient analysis of laminated composite shells. Journal of Reinforced Plastics and Composites, Vol.5(11): Nour-Omid, B. and Rankin, C. C Finite rotation analysis and consistent linearization using projectors. Computer Methods in Applied Mechanics and Engineering, Vol.93(3): Simo, J. and Tarnow, N New energy and momentum conserving algorithm for the non-linear dynamics of shells. International Journal for Numerical Methods in Engineering, Vol.37(15): Zhang, Y. and Kim, K A simple displacement-based 3-node triangular element for linear and geometrically nonlinear analysis of laminated composite plates. Computer Methods in Applied Mechanics and Engineering, Vol.194(45-47): RESPONSIBILITY NOTICE The authors are the only responsible for the printed material included in this paper.
Dynamic Response Of Laminated Composite Shells Subjected To Impulsive Loads
IOSR Journal of Mechanical and Civil Engineering (IOSR-JMCE) e-issn: 2278-1684,p-ISSN: 2320-334X, Volume 14, Issue 3 Ver. I (May. - June. 2017), PP 108-123 www.iosrjournals.org Dynamic Response Of Laminated
More informationCO-ROTATIONAL DYNAMIC FORMULATION FOR 2D BEAMS
COMPDYN 011 ECCOMAS Thematic Conference on Computational Methods in Structural Dynamics and Earthquake Engineering M. Papadrakakis, M. Fragiadakis, V. Plevris (eds.) Corfu, Greece, 5-8 May 011 CO-ROTATIONAL
More informationGeometrically exact beam dynamics, with and without rotational degree of freedom
ICCM2014 28-30 th July, Cambridge, England Geometrically exact beam dynamics, with and without rotational degree of freedom *Tien Long Nguyen¹, Carlo Sansour 2, and Mohammed Hjiaj 1 1 Department of Civil
More information. D CR Nomenclature D 1
. D CR Nomenclature D 1 Appendix D: CR NOMENCLATURE D 2 The notation used by different investigators working in CR formulations has not coalesced, since the topic is in flux. This Appendix identifies the
More informationNonlinear bending analysis of laminated composite stiffened plates
Nonlinear bending analysis of laminated composite stiffened plates * S.N.Patel 1) 1) Dept. of Civi Engineering, BITS Pilani, Pilani Campus, Pilani-333031, (Raj), India 1) shuvendu@pilani.bits-pilani.ac.in
More informationNONLINEAR STRUCTURAL DYNAMICS USING FE METHODS
NONLINEAR STRUCTURAL DYNAMICS USING FE METHODS Nonlinear Structural Dynamics Using FE Methods emphasizes fundamental mechanics principles and outlines a modern approach to understanding structural dynamics.
More informationThe Finite Element Method for Solid and Structural Mechanics
The Finite Element Method for Solid and Structural Mechanics Sixth edition O.C. Zienkiewicz, CBE, FRS UNESCO Professor of Numerical Methods in Engineering International Centre for Numerical Methods in
More informationAN ALTERNATIVE TECHNIQUE FOR TANGENTIAL STRESS CALCULATION IN DISCONTINUOUS BOUNDARY ELEMENTS
th Pan-American Congress of Applied Mechanics January 04-08, 00, Foz do Iguaçu, PR, Brazil AN ALTERNATIVE TECHNIQUE FOR TANGENTIAL STRESS CALCULATION IN DISCONTINUOUS BOUNDARY ELEMENTS Otávio Augusto Alves
More informationPost Graduate Diploma in Mechanical Engineering Computational mechanics using finite element method
9210-220 Post Graduate Diploma in Mechanical Engineering Computational mechanics using finite element method You should have the following for this examination one answer book scientific calculator No
More informationA consistent dynamic finite element formulation for a pipe using Euler parameters
111 A consistent dynamic finite element formulation for a pipe using Euler parameters Ara Arabyan and Yaqun Jiang Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ 85721,
More informationBending of Simply Supported Isotropic and Composite Laminate Plates
Bending of Simply Supported Isotropic and Composite Laminate Plates Ernesto Gutierrez-Miravete 1 Isotropic Plates Consider simply a supported rectangular plate of isotropic material (length a, width b,
More informationDYNAMIC FAILURE ANALYSIS OF LAMINATED COMPOSITE PLATES
Association of Metallurgical Engineers of Serbia AMES Scientific paper UDC:669.1-419:628.183=20 DYNAMIC FAILURE ANALYSIS OF LAMINATED COMPOSITE PLATES J. ESKANDARI JAM 1 and N. GARSHASBI NIA 2 1- Aerospace
More informationA NOTE ON RELATIONSHIP BETWEEN FIXED-POLE AND MOVING-POLE APPROACHES IN STATIC AND DYNAMIC ANALYSIS OF NON-LINEAR SPATIAL BEAM STRUCTURES
European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 212) J. Eberhardsteiner et.al. (eds.) Vienna, Austria, September 1-14, 212 A NOTE ON RELATIONSHIP BETWEEN FIXED-POLE
More informationMechanics of Inflatable Fabric Beams
Copyright c 2008 ICCES ICCES, vol.5, no.2, pp.93-98 Mechanics of Inflatable Fabric Beams C. Wielgosz 1,J.C.Thomas 1,A.LeVan 1 Summary In this paper we present a summary of the behaviour of inflatable fabric
More informationUNCONVENTIONAL FINITE ELEMENT MODELS FOR NONLINEAR ANALYSIS OF BEAMS AND PLATES
UNCONVENTIONAL FINITE ELEMENT MODELS FOR NONLINEAR ANALYSIS OF BEAMS AND PLATES A Thesis by WOORAM KIM Submitted to the Office of Graduate Studies of Texas A&M University in partial fulfillment of the
More informationNONLINEAR CONTINUUM FORMULATIONS CONTENTS
NONLINEAR CONTINUUM FORMULATIONS CONTENTS Introduction to nonlinear continuum mechanics Descriptions of motion Measures of stresses and strains Updated and Total Lagrangian formulations Continuum shell
More informationJEPPIAAR ENGINEERING COLLEGE
JEPPIAAR ENGINEERING COLLEGE Jeppiaar Nagar, Rajiv Gandhi Salai 600 119 DEPARTMENT OFMECHANICAL ENGINEERING QUESTION BANK VI SEMESTER ME6603 FINITE ELEMENT ANALYSIS Regulation 013 SUBJECT YEAR /SEM: III
More informationTheoretical Manual Theoretical background to the Strand7 finite element analysis system
Theoretical Manual Theoretical background to the Strand7 finite element analysis system Edition 1 January 2005 Strand7 Release 2.3 2004-2005 Strand7 Pty Limited All rights reserved Contents Preface Chapter
More informationStatic & Dynamic. Analysis of Structures. Edward L.Wilson. University of California, Berkeley. Fourth Edition. Professor Emeritus of Civil Engineering
Static & Dynamic Analysis of Structures A Physical Approach With Emphasis on Earthquake Engineering Edward LWilson Professor Emeritus of Civil Engineering University of California, Berkeley Fourth Edition
More informationFinite Element Method in Geotechnical Engineering
Finite Element Method in Geotechnical Engineering Short Course on + Dynamics Boulder, Colorado January 5-8, 2004 Stein Sture Professor of Civil Engineering University of Colorado at Boulder Contents Steps
More informationINTRODUCTION TO THE EXPLICIT FINITE ELEMENT METHOD FOR NONLINEAR TRANSIENT DYNAMICS
INTRODUCTION TO THE EXPLICIT FINITE ELEMENT METHOD FOR NONLINEAR TRANSIENT DYNAMICS SHEN R. WU and LEI GU WILEY A JOHN WILEY & SONS, INC., PUBLICATION ! PREFACE xv PARTI FUNDAMENTALS 1 1 INTRODUCTION 3
More informationGeneric Strategies to Implement Material Grading in Finite Element Methods for Isotropic and Anisotropic Materials
University of Nebraska - Lincoln DigitalCommons@University of Nebraska - Lincoln Engineering Mechanics Dissertations & Theses Mechanical & Materials Engineering, Department of Winter 12-9-2011 Generic
More informationINTERNATIONAL JOURNAL OF APPLIED ENGINEERING RESEARCH, DINDIGUL Volume 2, No 1, 2011
Interlaminar failure analysis of FRP cross ply laminate with elliptical cutout Venkateswara Rao.S 1, Sd. Abdul Kalam 1, Srilakshmi.S 1, Bala Krishna Murthy.V 2 1 Mechanical Engineering Department, P. V.
More informationDynamic and buckling analysis of FRP portal frames using a locking-free finite element
Fourth International Conference on FRP Composites in Civil Engineering (CICE8) 22-24July 8, Zurich, Switzerland Dynamic and buckling analysis of FRP portal frames using a locking-free finite element F.
More informationCOPYRIGHTED MATERIAL. Index
Index A Admissible function, 163 Amplification factor, 36 Amplitude, 1, 22 Amplitude-modulated carrier, 630 Amplitude ratio, 36 Antinodes, 612 Approximate analytical methods, 647 Assumed modes method,
More informationFLEXIBILITY METHOD FOR INDETERMINATE FRAMES
UNIT - I FLEXIBILITY METHOD FOR INDETERMINATE FRAMES 1. What is meant by indeterminate structures? Structures that do not satisfy the conditions of equilibrium are called indeterminate structure. These
More informationGeometric nonlinear sensitivity analysis for nonparametric shape optimization with non-zero prescribed displacements
0 th World Congress on Structural and Multidisciplinary Optimization May 9-24, 203, Orlando, Florida, USA Geometric nonlinear sensitivity analysis for nonparametric shape optimization with non-zero prescribed
More informationInternational Journal of Advanced Engineering Technology E-ISSN
Research Article INTEGRATED FORCE METHOD FOR FIBER REINFORCED COMPOSITE PLATE BENDING PROBLEMS Doiphode G. S., Patodi S. C.* Address for Correspondence Assistant Professor, Applied Mechanics Department,
More informationFinite Element Analysis Prof. Dr. B. N. Rao Department of Civil Engineering Indian Institute of Technology, Madras. Module - 01 Lecture - 13
Finite Element Analysis Prof. Dr. B. N. Rao Department of Civil Engineering Indian Institute of Technology, Madras (Refer Slide Time: 00:25) Module - 01 Lecture - 13 In the last class, we have seen how
More informationGyroscopic matrixes of the straight beams and the discs
Titre : Matrice gyroscopique des poutres droites et des di[...] Date : 29/05/2013 Page : 1/12 Gyroscopic matrixes of the straight beams and the discs Summarized: This document presents the formulation
More informationComputational non-linear structural dynamics and energy-momentum integration schemes
icccbe 2010 Nottingham University Press Proceedings of the International Conference on Computing in Civil and Building Engineering W Tizani (Editor) Computational non-linear structural dynamics and energy-momentum
More informationGeometry-dependent MITC method for a 2-node iso-beam element
Structural Engineering and Mechanics, Vol. 9, No. (8) 3-3 Geometry-dependent MITC method for a -node iso-beam element Phill-Seung Lee Samsung Heavy Industries, Seocho, Seoul 37-857, Korea Hyu-Chun Noh
More informationGEOMETRIC NONLINEAR ANALYSIS
GEOMETRIC NONLINEAR ANALYSIS The approach for solving problems with geometric nonlinearity is presented. The ESAComp solution relies on Elmer open-source computational tool [1] for multiphysics problems.
More informationLarge Thermal Deflections of a Simple Supported Beam with Temperature-Dependent Physical Properties
Large Thermal Deflections of a Simple Supported Beam with Temperature-Dependent Physical Properties DR. ŞEREF DOĞUŞCAN AKBAŞ Civil Engineer, Şehit Muhtar Mah. Öğüt Sok. No:2/37, 34435 Beyoğlu- Istanbul,
More informationVibration Behaviour of Laminated Composite Flat Panel Under Hygrothermal Environment
International Review of Applied Engineering Research. ISSN 2248-9967 Volume 4, Number 5 (2014), pp. 455-464 Research India Publications http://www.ripublication.com/iraer.htm Vibration Behaviour of Laminated
More informationPractice Final Examination. Please initial the statement below to show that you have read it
EN175: Advanced Mechanics of Solids Practice Final Examination School of Engineering Brown University NAME: General Instructions No collaboration of any kind is permitted on this examination. You may use
More informationVIBRATION PROBLEMS IN ENGINEERING
VIBRATION PROBLEMS IN ENGINEERING FIFTH EDITION W. WEAVER, JR. Professor Emeritus of Structural Engineering The Late S. P. TIMOSHENKO Professor Emeritus of Engineering Mechanics The Late D. H. YOUNG Professor
More informationEDEM DISCRETIZATION (Phase II) Normal Direction Structure Idealization Tangential Direction Pore spring Contact spring SPRING TYPES Inner edge Inner d
Institute of Industrial Science, University of Tokyo Bulletin of ERS, No. 48 (5) A TWO-PHASE SIMPLIFIED COLLAPSE ANALYSIS OF RC BUILDINGS PHASE : SPRING NETWORK PHASE Shanthanu RAJASEKHARAN, Muneyoshi
More informationBack Calculation of Rock Mass Modulus using Finite Element Code (COMSOL)
Back Calculation of Rock Mass Modulus using Finite Element Code (COMSOL) Amirreza Ghasemi 1. Introduction Deformability is recognized as one of the most important parameters governing the behavior of rock
More informationUltimate shear strength of FPSO stiffened panels after supply vessel collision
Ultimate shear strength of FPSO stiffened panels after supply vessel collision Nicolau Antonio dos Santos Rizzo PETROBRAS Rio de Janeiro Brazil Marcelo Caire SINTEF do Brasil Rio de Janeiro Brazil Carlos
More informationThe Finite Element Method for Mechonics of Solids with ANSYS Applicotions
The Finite Element Method for Mechonics of Solids with ANSYS Applicotions ELLIS H. DILL 0~~F~~~~"P Boca Raton London New Vork CRC Press is an imprint 01 the Taylor & Francis Group, an Informa business
More informationQUASI-STATIC AND DYNAMIC SIMULATION OF SHEET METAL FORMING PROCESSES USING LINEAR AND QUADRATIC SOLID- SHELL ELEMENTS
Proceedings of the 6th International Conference on Mechanics and Materials in Design, Editors: J.F. Silva Gomes & S.A. Meguid, P.Delgada/Azores, 26-30 July 2015 PAPER REF: 5456 QUASI-STATIC AND DYNAMIC
More informationME751 Advanced Computational Multibody Dynamics
ME751 Advanced Computational Multibody Dynamics October 24, 2016 Antonio Recuero University of Wisconsin-Madison Quote of the Day If a cluttered desk is a sign of a cluttered mind, of what, then, is an
More informationPrinciples of Finite Element for Design Engineers and Analysts. Ayman Shama, Ph.D., P.E., F.ASCE
Principles of Finite Element for Design Engineers and Analysts Ayman Shama, Ph.D., P.E., F.ASCE Outline Principles of Engineering Analysis The development of the finite element method Types of elements
More informationPLAT DAN CANGKANG (TKS 4219)
PLAT DAN CANGKANG (TKS 4219) SESI I: PLATES Dr.Eng. Achfas Zacoeb Dept. of Civil Engineering Brawijaya University INTRODUCTION Plates are straight, plane, two-dimensional structural components of which
More informationME751 Advanced Computational Multibody Dynamics
ME751 Advanced Computational Multibody Dynamics November 2, 2016 Antonio Recuero University of Wisconsin-Madison Quotes of the Day The methods which I set forth do not require either constructions or geometrical
More informationNUMERICAL ANALYSIS OF A PILE SUBJECTED TO LATERAL LOADS
IGC 009, Guntur, INDIA NUMERICAL ANALYSIS OF A PILE SUBJECTED TO LATERAL LOADS Mohammed Younus Ahmed Graduate Student, Earthquake Engineering Research Center, IIIT Hyderabad, Gachibowli, Hyderabad 3, India.
More informationEsben Byskov. Elementary Continuum. Mechanics for Everyone. With Applications to Structural Mechanics. Springer
Esben Byskov Elementary Continuum Mechanics for Everyone With Applications to Structural Mechanics Springer Contents Preface v Contents ix Introduction What Is Continuum Mechanics? "I Need Continuum Mechanics
More informationPresented By: EAS 6939 Aerospace Structural Composites
A Beam Theory for Laminated Composites and Application to Torsion Problems Dr. BhavaniV. Sankar Presented By: Sameer Luthra EAS 6939 Aerospace Structural Composites 1 Introduction Composite beams have
More informationSHELL STRUCTURES. THEORY AND APPLICATIONS
The 5th Conference SHELL STRUCTURES. THEORY AND APPLICATIONS Janowice * 15-18 October MODERATE ROTATION THEORY FEM ANALYSIS OF LAMINATED ANISOTROPIC COMPOSITE PLATES AND SHELLS I. Kreja 1 ) and R. Schmidt
More informationA FINITE ELEMENT MODEL FOR THE ANALYSIS OF DELAMINATIONS IN FRP SHELLS
TRENDS IN COMPUTATIONAL STRUCTURAL MECHANICS W.A. Wall, K.-U. Bletzinger and K. Schweizerhof (Eds.) c CIMNE, Barcelona, Spain 2001 A FINITE ELEMENT MODEL FOR THE ANALYSIS OF DELAMINATIONS IN FRP SHELLS
More informationNumerical simulation of the coil spring and investigation the impact of tension and compression to the spring natural frequencies
Numerical simulation of the coil spring and investigation the impact of tension and compression to the spring natural frequencies F. D. Sorokin 1, Zhou Su 2 Bauman Moscow State Technical University, Moscow,
More informationBENCHMARK LINEAR FINITE ELEMENT ANALYSIS OF LATERALLY LOADED SINGLE PILE USING OPENSEES & COMPARISON WITH ANALYTICAL SOLUTION
BENCHMARK LINEAR FINITE ELEMENT ANALYSIS OF LATERALLY LOADED SINGLE PILE USING OPENSEES & COMPARISON WITH ANALYTICAL SOLUTION Ahmed Elgamal and Jinchi Lu October 07 Introduction In this study: I) The response
More informationNon-linear and time-dependent material models in Mentat & MARC. Tutorial with Background and Exercises
Non-linear and time-dependent material models in Mentat & MARC Tutorial with Background and Exercises Eindhoven University of Technology Department of Mechanical Engineering Piet Schreurs July 7, 2009
More informationAeroelastic effects of large blade deflections for wind turbines
Aeroelastic effects of large blade deflections for wind turbines Torben J. Larsen Anders M. Hansen Risoe, National Laboratory Risoe, National Laboratory P.O. Box 49, 4 Roskilde, Denmark P.O. Box 49, 4
More informationBilinear Quadrilateral (Q4): CQUAD4 in GENESIS
Bilinear Quadrilateral (Q4): CQUAD4 in GENESIS The Q4 element has four nodes and eight nodal dof. The shape can be any quadrilateral; we ll concentrate on a rectangle now. The displacement field in terms
More information202 Index. failure, 26 field equation, 122 force, 1
Index acceleration, 12, 161 admissible function, 155 admissible stress, 32 Airy's stress function, 122, 124 d'alembert's principle, 165, 167, 177 amplitude, 171 analogy, 76 anisotropic material, 20 aperiodic
More informationCOMPUTATIONAL MODELING APPLIED TO THE STUDY OF THERMAL BUCKLING OF COLUMNS
COMPUTATIONAL MODELING APPLIED TO THE STUDY OF THERMAL BUCKLING OF COLUMNS R. da S. Michaello a, D. Helbig b, L. A. O. Rocha b, M. de V. Real c, E. D. dos Santos c, and L. A. Isoldi c a Universidade Federal
More informationBHAR AT HID AS AN ENGIN E ERI N G C O L L E G E NATTR A MPA LL I
BHAR AT HID AS AN ENGIN E ERI N G C O L L E G E NATTR A MPA LL I 635 8 54. Third Year M E C H A NICAL VI S E M ES TER QUE S T I ON B ANK Subject: ME 6 603 FIN I T E E LE ME N T A N A L YSIS UNI T - I INTRODUCTION
More informationBUCKLING AND POST-BUCKLING IN FILAMENT WOUND COMPOSITE TUBES UNDER TRANSVERSE COMPRESSION
2 th International Conference on Composite Materials Copenhagen, 19-24 th July 215 BUCKLING AND POST-BUCKLING IN FILAMENT WOUND COMPOSITE TUBES UNDER TRANSVERSE COMPRESSION José Humberto S. Almeida Jr.
More informationFREE VIBRATION OF AXIALLY LOADED FUNCTIONALLY GRADED SANDWICH BEAMS USING REFINED SHEAR DEFORMATION THEORY
FREE VIBRATION OF AXIALLY LOADED FUNCTIONALLY GRADED SANDWICH BEAMS USING REFINED SHEAR DEFORMATION THEORY Thuc P. Vo 1, Adelaja Israel Osofero 1, Marco Corradi 1, Fawad Inam 1 1 Faculty of Engineering
More informationFinite element vibration analysis of laminated composite folded plate structures
273 Finite element vibration analysis of laminated composite folded plate structures A. Guha Niyogi, M.K. Laha and P.K. Sinha Department of Aerospace Engineering, Indian Institute of Technology, Kharagpur
More informationSANDWICH COMPOSITE BEAMS for STRUCTURAL APPLICATIONS
SANDWICH COMPOSITE BEAMS for STRUCTURAL APPLICATIONS de Aguiar, José M., josemaguiar@gmail.com Faculdade de Tecnologia de São Paulo, FATEC-SP Centro Estadual de Educação Tecnológica Paula Souza. CEETEPS
More informationMECHANICS OF MATERIALS
Third E CHAPTER 2 Stress MECHANICS OF MATERIALS Ferdinand P. Beer E. Russell Johnston, Jr. John T. DeWolf Lecture Notes: J. Walt Oler Texas Tech University and Strain Axial Loading Contents Stress & Strain:
More informationContent. Department of Mathematics University of Oslo
Chapter: 1 MEK4560 The Finite Element Method in Solid Mechanics II (January 25, 2008) (E-post:torgeiru@math.uio.no) Page 1 of 14 Content 1 Introduction to MEK4560 3 1.1 Minimum Potential energy..............................
More informationNonlinear RC beam element model under combined action of axial, bending and shear
icccbe 21 Nottingham University Press Proceedings of the International Conference on Computing in Civil and Building ngineering W Tiani (ditor) Nonlinear RC beam element model under combined action of
More informationFINITE ELEMENT ANALYSIS OF TAPERED COMPOSITE PLATE GIRDER WITH A NON-LINEAR VARYING WEB DEPTH
Journal of Engineering Science and Technology Vol. 12, No. 11 (2017) 2839-2854 School of Engineering, Taylor s University FINITE ELEMENT ANALYSIS OF TAPERED COMPOSITE PLATE GIRDER WITH A NON-LINEAR VARYING
More informationAnalysis of thin plate structures using the absolute nodal coordinate formulation
345 Analysis of thin plate structures using the absolute nodal coordinate formulation K Dufva 1 and A A Shabana 2 1 Department of Mechanical Engineering, Lappeenranta University of echnology, Lappeenranta,
More informationMITOCW MITRES2_002S10nonlinear_lec15_300k-mp4
MITOCW MITRES2_002S10nonlinear_lec15_300k-mp4 The following content is provided under a Creative Commons license. Your support will help MIT OpenCourseWare continue to offer high quality educational resources
More informationSoftware Verification
EXAMPLE 1-026 FRAME MOMENT AND SHEAR HINGES EXAMPLE DESCRIPTION This example uses a horizontal cantilever beam to test the moment and shear hinges in a static nonlinear analysis. The cantilever beam has
More informationDevelopment DKMQ Shell Element with Five Degrees of Freedom per Nodal
International Journal of Mechanical Engineering and Robotics Research Vol. 6, No., May 7 Development DKMQ Shell Element with Five Degrees of Freedom per Nodal Herry Irpanni, Irwan Katili, and Imam J. Maknun
More informationAnalysis of asymmetric radial deformation in pipe with local wall thinning under internal pressure using strain energy method
Analysis of asymmetric radial deformation in pipe with local wall thinning under internal pressure using strain energy method V.M.F. Nascimento Departameto de ngenharia Mecânica TM, UFF, Rio de Janeiro
More informationFinite Element Analysis Prof. Dr. B. N. Rao Department of Civil Engineering Indian Institute of Technology, Madras. Module - 01 Lecture - 11
Finite Element Analysis Prof. Dr. B. N. Rao Department of Civil Engineering Indian Institute of Technology, Madras Module - 01 Lecture - 11 Last class, what we did is, we looked at a method called superposition
More informationThe stiffness of plates
The stiffness of plates 1. Introduction The word plate is a collective term for elements in which forces can be transferred in two directions. Floors, walls, bridge slabs and laminates are all plates.
More informationDynamic Model of a Badminton Stroke
ISEA 28 CONFERENCE Dynamic Model of a Badminton Stroke M. Kwan* and J. Rasmussen Department of Mechanical Engineering, Aalborg University, 922 Aalborg East, Denmark Phone: +45 994 9317 / Fax: +45 9815
More informationPassive Damping Characteristics of Carbon Epoxy Composite Plates
Journal of Materials Science and Engineering A 6 (-) 35-4 doi:.765/6-63/6.-.5 D DAVID PUBLISHING Passive Damping Characteristics of Carbon Epoxy Composite Plates Dileep Kumar K * and V V Subba Rao Faculty
More informationStructural Dynamics Lecture 4. Outline of Lecture 4. Multi-Degree-of-Freedom Systems. Formulation of Equations of Motions. Undamped Eigenvibrations.
Outline of Multi-Degree-of-Freedom Systems Formulation of Equations of Motions. Newton s 2 nd Law Applied to Free Masses. D Alembert s Principle. Basic Equations of Motion for Forced Vibrations of Linear
More informationNUMERICAL SIMULATION OF STEEL CATENARY RISER
SIMMEC/EMMCOMP 214 XI Simpósio de Mecânica Computacional II Encontro Mineiro de Modelagem Computacional Juiz De Fora, MG, 28-3 de Maio De 214 NUMERICAL SIMULATION OF STEEL CATENARY RISER Marcus V. S. Casagrande
More informationProceedings of the ASME th International Conference on Ocean, Offshore and Arctic Engineering OMAE2016 June 19-24, 2016, Busan, South Korea
Proceedings of the ASME 26 35th International Conference on Ocean, Offshore and Arctic Engineering OMAE26 June 9-24, 26, Busan, South Korea OMAE26-54554 LOCAL STRAIN AND STRESS CALCULATION METHODS OF IRREGULAR
More informationFig. 1. Circular fiber and interphase between the fiber and the matrix.
Finite element unit cell model based on ABAQUS for fiber reinforced composites Tian Tang Composites Manufacturing & Simulation Center, Purdue University West Lafayette, IN 47906 1. Problem Statement In
More informationVIBRATION CONTROL OF RECTANGULAR CROSS-PLY FRP PLATES USING PZT MATERIALS
Journal of Engineering Science and Technology Vol. 12, No. 12 (217) 3398-3411 School of Engineering, Taylor s University VIBRATION CONTROL OF RECTANGULAR CROSS-PLY FRP PLATES USING PZT MATERIALS DILEEP
More informationSemiloof Curved Thin Shell Elements
Semiloof Curved Thin Shell Elements General Element Name Y,v,θy X,u,θx Z,w,θz Element Group Element Subgroup Element Description Number Of Nodes Freedoms Node Coordinates TSL 1 2 Semiloof 3 QSL8 7 8 1
More informationSPECTRAL FINITE ELEMENT METHOD
SPECTRAL FINITE ELEMENT METHOD Originally proposed by Patera in 1984 for problems in fluid dynamics Adopted for problems of propagation of acoustic and seismic waves Snapshot of the propagation of seismic
More informationHIGHER-ORDER THEORIES
HIGHER-ORDER THEORIES THIRD-ORDER SHEAR DEFORMATION PLATE THEORY LAYERWISE LAMINATE THEORY J.N. Reddy 1 Third-Order Shear Deformation Plate Theory Assumed Displacement Field µ u(x y z t) u 0 (x y t) +
More informationVIBRATION AND DAMPING ANALYSIS OF FIBER REINFORCED COMPOSITE MATERIAL CONICAL SHELLS
VIBRATION AND DAMPING ANALYSIS OF FIBER REINFORCED COMPOSITE MATERIAL CONICAL SHELLS Mechanical Engineering Department, Indian Institute of Technology, New Delhi 110 016, India (Received 22 January 1992,
More informationDynamic Analysis of Laminated Composite Plate Structure with Square Cut-Out under Hygrothermal Load
Dynamic Analysis of Laminated Composite Plate Structure with Square Cut-Out under Hygrothermal Load Arun Mukherjee 1, Dr. Sreyashi Das (nee Pal) 2 and Dr. A. Guha Niyogi 3 1 PG student, 2 Asst. Professor,
More informationCHAPTER THREE SYMMETRIC BENDING OF CIRCLE PLATES
CHAPTER THREE SYMMETRIC BENDING OF CIRCLE PLATES * Governing equations in beam and plate bending ** Solution by superposition 1.1 From Beam Bending to Plate Bending 1.2 Governing Equations For Symmetric
More informationContinuum Mechanics and the Finite Element Method
Continuum Mechanics and the Finite Element Method 1 Assignment 2 Due on March 2 nd @ midnight 2 Suppose you want to simulate this The familiar mass-spring system l 0 l y i X y i x Spring length before/after
More informationStability Analysis of Laminated Composite Thin-Walled Beam Structures
Paper 224 Civil-Comp Press, 2012 Proceedings of the Eleventh International Conference on Computational Structures echnolog, B.H.V. opping, (Editor), Civil-Comp Press, Stirlingshire, Scotland Stabilit nalsis
More informationPREDICTION OF OUT-OF-PLANE FAILURE MODES IN CFRP
PREDICTION OF OUT-OF-PLANE FAILURE MODES IN CFRP R. R. Pinto 1, P. P. Camanho 2 1 INEGI - Instituto de Engenharia Mecanica e Gestao Industrial, Rua Dr. Roberto Frias, 4200-465, Porto, Portugal 2 DEMec,
More informationIntroduction to Continuous Systems. Continuous Systems. Strings, Torsional Rods and Beams.
Outline of Continuous Systems. Introduction to Continuous Systems. Continuous Systems. Strings, Torsional Rods and Beams. Vibrations of Flexible Strings. Torsional Vibration of Rods. Bernoulli-Euler Beams.
More informationHIGHER-ORDER THEORIES
HIGHER-ORDER THEORIES Third-order Shear Deformation Plate Theory Displacement and strain fields Equations of motion Navier s solution for bending Layerwise Laminate Theory Interlaminar stress and strain
More informationDepartment of Structural, Faculty of Civil Engineering, Architecture and Urban Design, State University of Campinas, Brazil
Blucher Mechanical Engineering Proceedings May 2014, vol. 1, num. 1 www.proceedings.blucher.com.br/evento/10wccm A SIMPLIFIED FORMULATION FOR STRESS AND TRACTION BOUNDARY IN- TEGRAL EQUATIONS USING THE
More informationMeasurement of deformation. Measurement of elastic force. Constitutive law. Finite element method
Deformable Bodies Deformation x p(x) Given a rest shape x and its deformed configuration p(x), how large is the internal restoring force f(p)? To answer this question, we need a way to measure deformation
More informationUniversity of Sheffield The development of finite elements for 3D structural analysis in fire
The development of finite elements for 3D structural analysis in fire Chaoming Yu, I. W. Burgess, Z. Huang, R. J. Plank Department of Civil and Structural Engineering StiFF 05/09/2006 3D composite structures
More informationConstitutive Equations
Constitutive quations David Roylance Department of Materials Science and ngineering Massachusetts Institute of Technology Cambridge, MA 0239 October 4, 2000 Introduction The modules on kinematics (Module
More informationDiscrete Analysis for Plate Bending Problems by Using Hybrid-type Penalty Method
131 Bulletin of Research Center for Computing and Multimedia Studies, Hosei University, 21 (2008) Published online (http://hdl.handle.net/10114/1532) Discrete Analysis for Plate Bending Problems by Using
More informationEmbedded Foundation with Different Parameters under Dynamic Excitations
13 th World Conference on Earthquake Engineering Vancouver, B.C., Canada August 1-6, 2004 Paper No. 2287 Embedded Foundation with Different Parameters under Dynamic Excitations Jaya K P 1 and Meher Prasad
More informationEffects of Structural Forces on the Dynamic Performance of High Speed Rotating Impellers.
Effects of Structural Forces on the Dynamic Performance of High Speed Rotating Impellers. G Shenoy 1, B S Shenoy 1 and Raj C Thiagarajan 2 * 1 Dept. of Mechanical & Mfg. Engineering, Manipal Institute
More informationIraq Ref. & Air. Cond. Dept/ Technical College / Kirkuk
International Journal of Scientific & Engineering Research, Volume 6, Issue 4, April-015 1678 Study the Increasing of the Cantilever Plate Stiffness by Using s Jawdat Ali Yakoob Iesam Jondi Hasan Ass.
More information