The Finite Element Method for Solid and Structural Mechanics

Size: px
Start display at page:

Download "The Finite Element Method for Solid and Structural Mechanics"

Transcription

1 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 Engineering, Barcelona Previously Director of the Institute for Numerical Methods in Engineering University of Wales Swansea R.L. Taylor Professor in the Graduate School Department of Civil and Environmental Engineering University of California at Berkeley Berkeley, California ELSEVIER BUTTERWORTH HEINEMANN AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO

2 Contents Preface xiii 1. General problems in solid mechanics and non-linearity Introduction Small deformation solid mechanics problems Variational forms for non-linear elasticity Weak forms of governing equations Concluding remarks 15 References Galerkin method of approximation - irreducible and mixed forms Introduction Finite element approximation - Galerkin method Numerical integration - quadrature Non-linear transient and steady-state problems Boundary conditions: non-linear problems Mixed or irreducible forms Non-linear quasi-harmonic field problems Typical examples of transient non-linear calculations Concluding remarks 43 References Solution of non-linear algebraic equations Introduction Iterative techniques General remarks - incremental and rate methods 58 References Inelastic and non-linear materials Introduction Viscoelasticity-history dependence of deformation Classical time-independent plasticity theory Computation of stress increments 80

3 viii Contents 4.5 Isotropic plasticity models Generalized plasticity Some examples of plastic computation Basic formulation of creep problems Viscoplasticity - a generalization Some special problems of brittle materials Non-uniqueness and localization in elasto-plastic deformations Non-linear quasi-harmonic field problems Concluding remarks 118 References Geometrically non-linear problems - finite deformation Introduction Governing equations Variational description for finite deformation Two-dimensional forms A three-field, mixed finite deformation formulation A mixed-enhanced finite deformation formulation Forces dependent on deformation - pressure loads Concluding remarks 155 References Material constitution for finite deformation Introduction Isotropic elasticity Isotropic viscoelasticity Plasticity models Incremental formulations Rate constitutive models Numerical examples Concluding remarks 185 References Treatment of constraints - contact and tied interfaces Introduction Node-node contact: Hertzian contact Tied interfaces Node-surface contact Surface-surface contact Numerical examples Concluding remarks 224 References Pseudo-rigid and rigid-flexible bodies Introduction Pseudo-rigid motions Rigid motions 230

4 Contents ix 8.4 Connecting a rigid body to aflexiblebody Multibody coupling by joints Numerical examples 240 References Discrete element methods Introduction Early DEM formulations Contact detection Contact constraints and boundary conditions Block deformability Time integration for discrete element methods Associated discontinuous modelling methodologies Unifying aspects of discrete element methods Concluding remarks 272 References Structural mechanics problems in one dimension - rods Introduction Governing equations Weak (Galerkin) forms for rods Finite element solution: Euler-Bernoulli rods Finite element solution: Timoshenko rods Forms without rotation parameters Moment resisting frames Concluding remarks 320 References Plate bending approximation: thin (Kirchhoff) plates and C\ continuity requirements Introduction The plate problem: thick and thin formulations Rectangular element with corner nodes (12 degrees of freedom) Quadrilateral and parallelogram elements Triangular element with corner nodes (9 degrees of freedom) Triangular element of the simplest form (6 degrees of freedom) The patch test - an analytical requirement Numerical examples General remarks Singular shape functions for the simple triangular element An 18 degree-of-freedom triangular element with conforming shape functions Compatible quadrilateral elements Quasi-conforming elements Hermitian rectangle shape function The 21 and 18 degree-of-freedom triangle Mixed formulations - general remarks 366

5 x Contents Hybrid plate elements Discrete Kirchhoff constraints Rotation-free elements Inelastic material behaviour Concluding remarks - which elements? 376 References 'Thick' Reissner-Mindlin plates - irreducible and mixed formulations Introduction The irreducible formulation - reduced integration Mixed formulation for thick plates The patch test for plate bending elements Elements with discrete collocation constraints Elements with rotational bubble or enhanced modes Linked interpolation - an improvement of accuracy Discrete'exact'thin plate limit Performance of various 'thick' plate elements - limitations of thin plate theory Inelastic material behaviour Concluding remarks - adaptive refinement 420 References Shells as an assembly of flat elements Introduction Stiffness of a plane element in local coordinates Transformation to global coordinates and assembly of elements Local direction cosines 'Drilling' rotational stiffness - 6 degree-of-freedom assembly Elements with mid-side slope connections only Choice of element Practical examples 441 References Curved rods and axisymmetric shells Introduction Straight element Curved elements Independent slope-displacement interpolation with penalty functions (thick or thin shell formulations) 468 References Shells as a special case of three-dimensional analysis - Reissner-Mindlin assumptions Introduction Shell element with displacement and rotation parameters Special case of axisymmetric, curved, thick shells Special case of thick plates 487

6 Contents xi 15.5 Convergence Inelastic behaviour Some shell examples Concluding remarks 493 References Semi-analytical finite element processes - use of orthogonal functions and 'finite strip' methods Introduction Prismatic bar Thin membrane box structures Plates and boxes with flexure Axisymmetric solids with non-symmetrical load Axisymmetric shells with non-symmetrical load Concluding remarks 514 References Non-linear structural problems - large displacement and instability Introduction Large displacement theory of beams Elastic stability - energy interpretation Large displacement theory of thick plates Large displacement theory of thin plates Solution of large deflection problems Shells Concluding remarks 542 References Multiscale modelling Introduction Asymptotic analysis Statement of the problem and assumptions Formalism of the homogenization procedure Global solution Local approximation of the stress vector Finite element analysis applied to the local problem The non-linear case and bridging over several scales Asymptotic homogenization at three levels: micro, meso and macro Recovery of the micro description of the variables of the problem Material characteristics and homogenization results Multilevel procedures which use homogenization as an ingredient General first-order and second-order procedures Discrete-to-continuum linkage Local analysis of a unit cell Homogenization procedure - definition of successive yield surfaces 578

7 xii Contents Numerically developed global self-consistent elastic-plastic constitutive law Global solution and stress-recovery procedure Concluding remarks 586 References Computer procedures for finite element analysis Introduction Solution of non-linear problems Eigensolutions Restart option Concluding remarks 595 References 595 Appendix A Isoparametric finite element approximations 597 Appendix B Invariants of second-order tensors 604 Author index 609 Subject index 619

Using MATLAB and. Abaqus. Finite Element Analysis. Introduction to. Amar Khennane. Taylor & Francis Croup. Taylor & Francis Croup,

Using MATLAB and. Abaqus. Finite Element Analysis. Introduction to. Amar Khennane. Taylor & Francis Croup. Taylor & Francis Croup, Introduction to Finite Element Analysis Using MATLAB and Abaqus Amar Khennane Taylor & Francis Croup Boca Raton London New York CRC Press is an imprint of the Taylor & Francis Croup, an informa business

More information

Nonlinear Problems of Elasticity

Nonlinear Problems of Elasticity Stuart S. Antman Nonlinear Problems of Elasticity With 105 Illustrations Springer-Verlag New York Berlin Heidelberg London Paris Tokyo Hong Kong Barcelona Budapest Contents Preface vn Chapter I. Background

More information

Static & Dynamic. Analysis of Structures. Edward L.Wilson. University of California, Berkeley. Fourth Edition. Professor Emeritus of Civil Engineering

Static & 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 information

INTRODUCTION TO THE EXPLICIT FINITE ELEMENT METHOD FOR NONLINEAR TRANSIENT DYNAMICS

INTRODUCTION 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 information

COPYRIGHTED MATERIAL. Index

COPYRIGHTED 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 information

Theoretical Manual Theoretical background to the Strand7 finite element analysis system

Theoretical 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 information

Table of Contents. Preface... 13

Table of Contents. Preface... 13 Table of Contents Preface... 13 Chapter 1. Vibrations of Continuous Elastic Solid Media... 17 1.1. Objective of the chapter... 17 1.2. Equations of motion and boundary conditions of continuous media...

More information

VIBRATION PROBLEMS IN ENGINEERING

VIBRATION 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 information

An Introduction to the Finite Element Method

An Introduction to the Finite Element Method An Introduction to the Finite Element Method Third Edition J. N. REDDY Department 01 Mechanical Engineering Texas A&M University College Station, Texas, USA 77843 11 Boston Burr Ridge, IL Dubuque, IA Madison,

More information

System Dynamics for Engineering Students Concepts and Applications

System Dynamics for Engineering Students Concepts and Applications System Dynamics for Engineering Students Concepts and Applications Nicolae Lobontiu University of Alaska Anchorage "Ж AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE

More information

JEPPIAAR ENGINEERING COLLEGE

JEPPIAAR 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 information

The Finite Element Method for Mechonics of Solids with ANSYS Applicotions

The 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 information

Aircraft Structures Kirchhoff-Love Plates

Aircraft Structures Kirchhoff-Love Plates University of Liège erospace & Mechanical Engineering ircraft Structures Kirchhoff-Love Plates Ludovic Noels Computational & Multiscale Mechanics of Materials CM3 http://www.ltas-cm3.ulg.ac.be/ Chemin

More information

Esben 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 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 information

ANALYSIS RADIAL FOLDED PLATE

ANALYSIS RADIAL FOLDED PLATE ANALYSIS RADIAL FOLDED PLATE Ms.Pranoti Satish Bhamare 1, Prajakta S. Bramhankar 2, Pooja G. Baviskar 3 1,2,3 Assistant Professor, Department of Civil Engineering, Guru Gobind Singh College of Engineering

More information

FLEXIBILITY METHOD FOR INDETERMINATE FRAMES

FLEXIBILITY 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 information

Microstructural Randomness and Scaling in Mechanics of Materials. Martin Ostoja-Starzewski. University of Illinois at Urbana-Champaign

Microstructural Randomness and Scaling in Mechanics of Materials. Martin Ostoja-Starzewski. University of Illinois at Urbana-Champaign Microstructural Randomness and Scaling in Mechanics of Materials Martin Ostoja-Starzewski University of Illinois at Urbana-Champaign Contents Preface ix 1. Randomness versus determinism ix 2. Randomness

More information

Level 7 Postgraduate Diploma in Engineering Computational mechanics using finite element method

Level 7 Postgraduate Diploma in Engineering Computational mechanics using finite element method 9210-203 Level 7 Postgraduate Diploma in Engineering Computational mechanics using finite element method You should have the following for this examination one answer book No additional data is attached

More information

Introduction. Finite and Spectral Element Methods Using MATLAB. Second Edition. C. Pozrikidis. University of Massachusetts Amherst, USA

Introduction. Finite and Spectral Element Methods Using MATLAB. Second Edition. C. Pozrikidis. University of Massachusetts Amherst, USA Introduction to Finite and Spectral Element Methods Using MATLAB Second Edition C. Pozrikidis University of Massachusetts Amherst, USA (g) CRC Press Taylor & Francis Group Boca Raton London New York CRC

More information

Analysis Handbook. Metal Fatigue. for Computer-Aided Engineering. Barkey. Yung-Li Lee. Practical Problem-Solving Techniques. Hong-Tae Kang. Mark E.

Analysis Handbook. Metal Fatigue. for Computer-Aided Engineering. Barkey. Yung-Li Lee. Practical Problem-Solving Techniques. Hong-Tae Kang. Mark E. Metal Fatigue Analysis Handbook Practical Problem-Solving Techniques for Computer-Aided Engineering Yung-Li Lee Mark E. Barkey Hong-Tae Kang ms- ELSEVIER AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD

More information

BHAR 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 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 information

APPLIED PARTIAL DIFFERENTIAL EQUATIONS

APPLIED PARTIAL DIFFERENTIAL EQUATIONS APPLIED PARTIAL DIFFERENTIAL EQUATIONS AN I N T R O D U C T I O N ALAN JEFFREY University of Newcastle-upon-Tyne ACADEMIC PRESS An imprint of Elsevier Science Amsterdam Boston London New York Oxford Paris

More information

Differential Equations with Mathematica

Differential Equations with Mathematica Differential Equations with Mathematica THIRD EDITION Martha L. Abell James P. Braselton ELSEVIER ACADEMIC PRESS Amsterdam Boston Heidelberg London New York Oxford Paris San Diego San Francisco Singapore

More information

INTRODUCTION TO THE CALCULUS OF VARIATIONS AND ITS APPLICATIONS

INTRODUCTION TO THE CALCULUS OF VARIATIONS AND ITS APPLICATIONS INTRODUCTION TO THE CALCULUS OF VARIATIONS AND ITS APPLICATIONS Frederick Y.M. Wan University of California, Irvine CHAPMAN & HALL I(J)P An International Thomson Publishing Company New York Albany Bonn

More information

PLAT DAN CANGKANG (TKS 4219)

PLAT 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 information

Vibration Dynamics and Control

Vibration Dynamics and Control Giancarlo Genta Vibration Dynamics and Control Spri ringer Contents Series Preface Preface Symbols vii ix xxi Introduction 1 I Dynamics of Linear, Time Invariant, Systems 23 1 Conservative Discrete Vibrating

More information

Table of Contents. Preface...xvii. Part 1. Level

Table of Contents. Preface...xvii. Part 1. Level Preface...xvii Part 1. Level 1... 1 Chapter 1. The Basics of Linear Elastic Behavior... 3 1.1. Cohesion forces... 4 1.2. The notion of stress... 6 1.2.1. Definition... 6 1.2.2. Graphical representation...

More information

GEOPHYSICAL INVERSE THEORY AND REGULARIZATION PROBLEMS

GEOPHYSICAL INVERSE THEORY AND REGULARIZATION PROBLEMS Methods in Geochemistry and Geophysics, 36 GEOPHYSICAL INVERSE THEORY AND REGULARIZATION PROBLEMS Michael S. ZHDANOV University of Utah Salt Lake City UTAH, U.S.A. 2OO2 ELSEVIER Amsterdam - Boston - London

More information

Finite element modelling of structural mechanics problems

Finite element modelling of structural mechanics problems 1 Finite element modelling of structural mechanics problems Kjell Magne Mathisen Department of Structural Engineering Norwegian University of Science and Technology Lecture 10: Geilo Winter School - January,

More information

COSSERAT THEORIES: SHELLS, RODS AND POINTS

COSSERAT THEORIES: SHELLS, RODS AND POINTS COSSERAT THEORIES: SHELLS, RODS AND POINTS SOLID MECHANICS AND ITS APPLICATIONS Volume 79 Series Editor: G.M.L. GLADWELL Department of Civil Engineering University of Waterloo Waterloo, Ontario, Canada

More information

Bilinear Quadrilateral (Q4): CQUAD4 in GENESIS

Bilinear 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 information

GAME PHYSICS ENGINE DEVELOPMENT

GAME PHYSICS ENGINE DEVELOPMENT GAME PHYSICS ENGINE DEVELOPMENT IAN MILLINGTON i > AMSTERDAM BOSTON HEIDELBERG fpf l LONDON. NEW YORK. OXFORD ^. PARIS SAN DIEGO SAN FRANCISCO втс^н Г^ 4.«Mt-fSSKHbe. SINGAPORE. SYDNEY. TOKYO ELSEVIER

More information

Chapter 6 2D Elements Plate Elements

Chapter 6 2D Elements Plate Elements Institute of Structural Engineering Page 1 Chapter 6 2D Elements Plate Elements Method of Finite Elements I Institute of Structural Engineering Page 2 Continuum Elements Plane Stress Plane Strain Toda

More information

MODELING OF ELASTO-PLASTIC MATERIALS IN FINITE ELEMENT METHOD

MODELING OF ELASTO-PLASTIC MATERIALS IN FINITE ELEMENT METHOD MODELING OF ELASTO-PLASTIC MATERIALS IN FINITE ELEMENT METHOD Andrzej Skrzat, Rzeszow University of Technology, Powst. Warszawy 8, Rzeszow, Poland Abstract: User-defined material models which can be used

More information

UNCONVENTIONAL FINITE ELEMENT MODELS FOR NONLINEAR ANALYSIS OF BEAMS AND PLATES

UNCONVENTIONAL 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 information

Structural Dynamics Lecture Eleven: Dynamic Response of MDOF Systems: (Chapter 11) By: H. Ahmadian

Structural Dynamics Lecture Eleven: Dynamic Response of MDOF Systems: (Chapter 11) By: H. Ahmadian Structural Dynamics Lecture Eleven: Dynamic Response of MDOF Systems: (Chapter 11) By: H. Ahmadian ahmadian@iust.ac.ir Dynamic Response of MDOF Systems: Mode-Superposition Method Mode-Superposition Method:

More information

Contents. Prologue Introduction. Classical Approximation... 19

Contents. Prologue Introduction. Classical Approximation... 19 Contents Prologue........................................................................ 15 1 Introduction. Classical Approximation.................................. 19 1.1 Introduction................................................................

More information

Development of discontinuous Galerkin method for linear strain gradient elasticity

Development of discontinuous Galerkin method for linear strain gradient elasticity Development of discontinuous Galerkin method for linear strain gradient elasticity R Bala Chandran Computation for Design and Optimizaton Massachusetts Institute of Technology Cambridge, MA L. Noels* Aerospace

More information

ELASTICITY AND FRACTURE MECHANICS. Vijay G. Ukadgaonker

ELASTICITY AND FRACTURE MECHANICS. Vijay G. Ukadgaonker THEORY OF ELASTICITY AND FRACTURE MECHANICS y x Vijay G. Ukadgaonker Theory of Elasticity and Fracture Mechanics VIJAY G. UKADGAONKER Former Professor Indian Institute of Technology Bombay Delhi-110092

More information

Effect of Specimen Dimensions on Flexural Modulus in a 3-Point Bending Test

Effect of Specimen Dimensions on Flexural Modulus in a 3-Point Bending Test Effect of Specimen Dimensions on Flexural Modulus in a 3-Point Bending Test M. Praveen Kumar 1 and V. Balakrishna Murthy 2* 1 Mechanical Engineering Department, P.V.P. Siddhartha Institute of Technology,

More information

Nonlinear bending analysis of laminated composite stiffened plates

Nonlinear 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 information

Boundary. DIFFERENTIAL EQUATIONS with Fourier Series and. Value Problems APPLIED PARTIAL. Fifth Edition. Richard Haberman PEARSON

Boundary. DIFFERENTIAL EQUATIONS with Fourier Series and. Value Problems APPLIED PARTIAL. Fifth Edition. Richard Haberman PEARSON APPLIED PARTIAL DIFFERENTIAL EQUATIONS with Fourier Series and Boundary Value Problems Fifth Edition Richard Haberman Southern Methodist University PEARSON Boston Columbus Indianapolis New York San Francisco

More information

ME 1401 FINITE ELEMENT ANALYSIS UNIT I PART -A. 2. Why polynomial type of interpolation functions is mostly used in FEM?

ME 1401 FINITE ELEMENT ANALYSIS UNIT I PART -A. 2. Why polynomial type of interpolation functions is mostly used in FEM? SHRI ANGALAMMAN COLLEGE OF ENGINEERING AND TECHNOLOGY (An ISO 9001:2008 Certified Institution) SIRUGANOOR, TIRUCHIRAPPALLI 621 105 Department of Mechanical Engineering ME 1401 FINITE ELEMENT ANALYSIS 1.

More information

Department of Structural, Faculty of Civil Engineering, Architecture and Urban Design, State University of Campinas, Brazil

Department 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 information

Elasto-Plastic and Damage Analysis of Plates and Shells

Elasto-Plastic and Damage Analysis of Plates and Shells Elasto-Plastic and Damage Analysis of Plates and Shells George Z. Voyiadjis Pawel Woelke Elasto-Plastic and Damage Analysis of Plates and Shells With 82 Figures and 14 Tables 123 Dr. George Z. Voyiadjis

More information

ELASTOPLASTIC STEEL BEAM BENDING ANALYSIS BY USING ABAQUS

ELASTOPLASTIC STEEL BEAM BENDING ANALYSIS BY USING ABAQUS 11 ELASTOPLASTIC STEEL BEAM BENDING ANALYSIS BY USING ABAQUS Biswajit Jena * * Corresponding author: biswa.tech88@gmail.com Abstract: In recent years tremendous efforts have been made in development of

More information

Partial Differential Equations and the Finite Element Method

Partial Differential Equations and the Finite Element Method Partial Differential Equations and the Finite Element Method Pavel Solin The University of Texas at El Paso Academy of Sciences ofthe Czech Republic iwiley- INTERSCIENCE A JOHN WILEY & SONS, INC, PUBLICATION

More information

Chapter 5 Structural Elements: The truss & beam elements

Chapter 5 Structural Elements: The truss & beam elements Institute of Structural Engineering Page 1 Chapter 5 Structural Elements: The truss & beam elements Institute of Structural Engineering Page 2 Chapter Goals Learn how to formulate the Finite Element Equations

More information

Code No: RT41033 R13 Set No. 1 IV B.Tech I Semester Regular Examinations, November - 2016 FINITE ELEMENT METHODS (Common to Mechanical Engineering, Aeronautical Engineering and Automobile Engineering)

More information

NONLINEAR STRUCTURAL DYNAMICS USING FE METHODS

NONLINEAR 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 information

Chapter 12 Plate Bending Elements. Chapter 12 Plate Bending Elements

Chapter 12 Plate Bending Elements. Chapter 12 Plate Bending Elements CIVL 7/8117 Chapter 12 - Plate Bending Elements 1/34 Chapter 12 Plate Bending Elements Learning Objectives To introduce basic concepts of plate bending. To derive a common plate bending element stiffness

More information

Feature Extraction and Image Processing

Feature Extraction and Image Processing Feature Extraction and Image Processing Second edition Mark S. Nixon Alberto S. Aguado :*авш JBK IIP AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO

More information

MAE 323: Chapter 6. Structural Models

MAE 323: Chapter 6. Structural Models Common element types for structural analyis: oplane stress/strain, Axisymmetric obeam, truss,spring oplate/shell elements o3d solid ospecial: Usually used for contact or other constraints What you need

More information

CRITERIA FOR SELECTION OF FEM MODELS.

CRITERIA FOR SELECTION OF FEM MODELS. CRITERIA FOR SELECTION OF FEM MODELS. Prof. P. C.Vasani,Applied Mechanics Department, L. D. College of Engineering,Ahmedabad- 380015 Ph.(079) 7486320 [R] E-mail:pcv-im@eth.net 1. Criteria for Convergence.

More information

An Introduction to Stochastic Modeling

An Introduction to Stochastic Modeling F An Introduction to Stochastic Modeling Fourth Edition Mark A. Pinsky Department of Mathematics Northwestern University Evanston, Illinois Samuel Karlin Department of Mathematics Stanford University Stanford,

More information

Semiloof Curved Thin Shell Elements

Semiloof 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 information

Finite Element Method

Finite Element Method Finite Element Method Finite Element Method (ENGC 6321) Syllabus Objectives Understand the basic theory of the FEM Know the behaviour and usage of each type of elements covered in this course one dimensional

More information

MITOCW MITRES2_002S10linear_lec07_300k-mp4

MITOCW MITRES2_002S10linear_lec07_300k-mp4 MITOCW MITRES2_002S10linear_lec07_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 information

Discrete Analysis for Plate Bending Problems by Using Hybrid-type Penalty Method

Discrete 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 information

Contents as of 12/8/2017. Preface. 1. Overview...1

Contents as of 12/8/2017. Preface. 1. Overview...1 Contents as of 12/8/2017 Preface 1. Overview...1 1.1 Introduction...1 1.2 Finite element data...1 1.3 Matrix notation...3 1.4 Matrix partitions...8 1.5 Special finite element matrix notations...9 1.6 Finite

More information

Quintic beam closed form matrices (revised 2/21, 2/23/12) General elastic beam with an elastic foundation

Quintic beam closed form matrices (revised 2/21, 2/23/12) General elastic beam with an elastic foundation General elastic beam with an elastic foundation Figure 1 shows a beam-column on an elastic foundation. The beam is connected to a continuous series of foundation springs. The other end of the foundation

More information

CHAPTER 14 BUCKLING ANALYSIS OF 1D AND 2D STRUCTURES

CHAPTER 14 BUCKLING ANALYSIS OF 1D AND 2D STRUCTURES CHAPTER 14 BUCKLING ANALYSIS OF 1D AND 2D STRUCTURES 14.1 GENERAL REMARKS In structures where dominant loading is usually static, the most common cause of the collapse is a buckling failure. Buckling may

More information

Contents. I Introduction 1. Preface. xiii

Contents. I Introduction 1. Preface. xiii Contents Preface xiii I Introduction 1 1 Continuous matter 3 1.1 Molecules................................ 4 1.2 The continuum approximation.................... 6 1.3 Newtonian mechanics.........................

More information

Uncorrected Proof Available online at

Uncorrected Proof Available online at Available online at www.sciencedirect.com ScienceDirect Procedia Engineering00 (2017) 000 000 www.elsevier.com/locate/procedia Sustainable Civil Engineering Structures and Construction Materials, SCESCM

More information

INELASTIC BUCKLING ANALYSIS OF AXIALLY COMPRESSED THIN CCCC PLATES USING TAYLOR-MACLAURIN DISPLACEMENT FUNCTION

INELASTIC BUCKLING ANALYSIS OF AXIALLY COMPRESSED THIN CCCC PLATES USING TAYLOR-MACLAURIN DISPLACEMENT FUNCTION ISSN-L: 2223-553, ISSN: 2223-44 Vol 4 No 6 November 2013 INELASTIC BUCKLING ANALYSIS OF AXIALLY COMPRESSED THIN CCCC PLATES USING TAYLOR-MACLAURIN DISPLACEMENT FUNCTION O M Ibearugbulem 1, D O Onwuka 2,

More information

GAME PHYSICS SECOND EDITION. дяййтаййг 1 *

GAME PHYSICS SECOND EDITION. дяййтаййг 1 * GAME PHYSICS SECOND EDITION DAVID H. EBERLY дяййтаййг 1 * К AMSTERDAM BOSTON HEIDELBERG LONDON NEW YORK OXFORD PARIS SAN DIEGO SAN FRANCISCO SINGAPORE SYDNEY TOKYO MORGAN ELSEVIER Morgan Kaufmann Publishers

More information

Theory of Elasticity. <gl Spri ringer. and Thermal Stresses. Explanations, Problems and Solutions. Jozef Ignaczak. Naotake Noda Yoshinobu Tanigawa

Theory of Elasticity. <gl Spri ringer. and Thermal Stresses. Explanations, Problems and Solutions. Jozef Ignaczak. Naotake Noda Yoshinobu Tanigawa M. Reza Eslami Richard B. Hetnarski Jozef Ignaczak Naobumi Sumi Naotake Noda Yoshinobu Tanigawa Theory of Elasticity and Thermal Stresses Explanations, Problems and Solutions

More information

HANDBUCH DER PHYSIK HERAUSGEGEBEN VON S. FLÜGGE. BAND VIa/2 FESTKÖRPERMECHANIK II BANDHERAUSGEBER C.TRUESDELL MIT 25 FIGUREN

HANDBUCH DER PHYSIK HERAUSGEGEBEN VON S. FLÜGGE. BAND VIa/2 FESTKÖRPERMECHANIK II BANDHERAUSGEBER C.TRUESDELL MIT 25 FIGUREN HANDBUCH DER PHYSIK HERAUSGEGEBEN VON S. FLÜGGE BAND VIa/2 FESTKÖRPERMECHANIK II BANDHERAUSGEBER C.TRUESDELL MIT 25 FIGUREN SPRINGER-VERLAG BERLIN HEIDELBERG NEWYORK 1972 Contents. The Linear Theory of

More information

in this web service Cambridge University Press

in this web service Cambridge University Press CONTINUUM MECHANICS This is a modern textbook for courses in continuum mechanics. It provides both the theoretical framework and the numerical methods required to model the behavior of continuous materials.

More information

MIXED RECTANGULAR FINITE ELEMENTS FOR PLATE BENDING

MIXED RECTANGULAR FINITE ELEMENTS FOR PLATE BENDING 144 MIXED RECTANGULAR FINITE ELEMENTS FOR PLATE BENDING J. N. Reddy* and Chen-Shyh-Tsay School of Aerospace, Mechanical and Nuclear Engineering, University of Oklahoma, Norman, Oklahoma The paper describes

More information

202 Index. failure, 26 field equation, 122 force, 1

202 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 information

Mechanics PhD Preliminary Spring 2017

Mechanics PhD Preliminary Spring 2017 Mechanics PhD Preliminary Spring 2017 1. (10 points) Consider a body Ω that is assembled by gluing together two separate bodies along a flat interface. The normal vector to the interface is given by n

More information

A MIXED TRIANGULAR ELEMENT FOR THE ELASTO-PLASTIC ANALYSIS OF KIRCHHOFF PLATES

A MIXED TRIANGULAR ELEMENT FOR THE ELASTO-PLASTIC ANALYSIS OF KIRCHHOFF PLATES COMPUTATIONAL MECHANICS New Trends and Applications S. Idelsohn, E. Oñate and E. Dvorkin (Eds.) c CIMNE, Barcelona, Spain 1998 A MIXED TRIANGULAR ELEMENT FOR THE ELASTO-PLASTIC ANALYSIS OF KIRCHHOFF PLATES

More information

FINITE GRID SOLUTION FOR NON-RECTANGULAR PLATES

FINITE GRID SOLUTION FOR NON-RECTANGULAR PLATES th International Conference on Earthquake Geotechnical Engineering June 5-8, 7 Paper No. 11 FINITE GRID SOLUTION FOR NON-RECTANGULAR PLATES A.Halim KARAŞĐN 1, Polat GÜLKAN ABSTRACT Plates on elastic foundations

More information

Wave Propagation in Anisotropic, Anelastic, Porous and Electromagnetic Media

Wave Propagation in Anisotropic, Anelastic, Porous and Electromagnetic Media SECTION I. SEISMIC EXPLORATION Volume 38 WAVE FIELDS IN REAL MEDIA: Wave Propagation in Anisotropic, Anelastic, Porous and Electromagnetic Media (SECOND EDITION, REVISED AND EXTENDED) by Jose M. CARCIONE

More information

An Atomistic-based Cohesive Zone Model for Quasi-continua

An Atomistic-based Cohesive Zone Model for Quasi-continua An Atomistic-based Cohesive Zone Model for Quasi-continua By Xiaowei Zeng and Shaofan Li Department of Civil and Environmental Engineering, University of California, Berkeley, CA94720, USA Extended Abstract

More information

Fundamentals of Nuclear Reactor Physics

Fundamentals of Nuclear Reactor Physics Fundamentals of Nuclear Reactor Physics E. E. Lewis Professor of Mechanical Engineering McCormick School of Engineering and Applied Science Northwestern University AMSTERDAM BOSTON HEIDELBERG LONDON NEW

More information

Application of pseudo-symmetric technique in dynamic analysis of concrete gravity dams

Application of pseudo-symmetric technique in dynamic analysis of concrete gravity dams Application of pseudo-symmetric technique in dynamic analysis of concrete gravity dams V. Lotfi Department of Civil and Environmental Engineering, Amirkabir University, Iran Abstract A new approach is

More information

M.S Comprehensive Examination Analysis

M.S Comprehensive Examination Analysis UNIVERSITY OF CALIFORNIA, BERKELEY Spring Semester 2014 Dept. of Civil and Environmental Engineering Structural Engineering, Mechanics and Materials Name:......................................... M.S Comprehensive

More information

FINITE ELEMENT ANALYSIS OF COMPOSITE MATERIALS

FINITE ELEMENT ANALYSIS OF COMPOSITE MATERIALS FINITE ELEMENT ANALYSIS OF COMPOSITE MATERIALS Ever J. Barbero Department of Mechanical and Aerospace Engineering West Virginia University USA CRC Press Taylor &.Francis Group Boca Raton London New York

More information

Statics and Influence Functions From a Modern Perspective

Statics and Influence Functions From a Modern Perspective Statics and Influence Functions From a Modern Perspective Friedel Hartmann Peter Jahn Statics and Influence Functions From a Modern Perspective 123 Friedel Hartmann Department of Civil Engineering University

More information

Dynamic Analysis of Coupling Vehicle-Bridge System Using Finite Prism Method

Dynamic Analysis of Coupling Vehicle-Bridge System Using Finite Prism Method Dynamic Analysis of Coupling Vehicle-Bridge System Using Finite Prism Method A. T. Saeed and Zhongfu Xiang Abstract To investigate the transient responses of bridges under moving vehicles, Finite Prism

More information

Chapter 2 Finite Element Formulations

Chapter 2 Finite Element Formulations Chapter 2 Finite Element Formulations The governing equations for problems solved by the finite element method are typically formulated by partial differential equations in their original form. These are

More information

Dynamic Systems. Modeling and Analysis. Hung V. Vu. Ramin S. Esfandiari. THE McGRAW-HILL COMPANIES, INC. California State University, Long Beach

Dynamic Systems. Modeling and Analysis. Hung V. Vu. Ramin S. Esfandiari. THE McGRAW-HILL COMPANIES, INC. California State University, Long Beach Dynamic Systems Modeling and Analysis Hung V. Vu California State University, Long Beach Ramin S. Esfandiari California State University, Long Beach THE McGRAW-HILL COMPANIES, INC. New York St. Louis San

More information

General elastic beam with an elastic foundation

General elastic beam with an elastic foundation General elastic beam with an elastic foundation Figure 1 shows a beam-column on an elastic foundation. The beam is connected to a continuous series of foundation springs. The other end of the foundation

More information

A HIGHER-ORDER BEAM THEORY FOR COMPOSITE BOX BEAMS

A HIGHER-ORDER BEAM THEORY FOR COMPOSITE BOX BEAMS A HIGHER-ORDER BEAM THEORY FOR COMPOSITE BOX BEAMS A. Kroker, W. Becker TU Darmstadt, Department of Mechanical Engineering, Chair of Structural Mechanics Hochschulstr. 1, D-64289 Darmstadt, Germany kroker@mechanik.tu-darmstadt.de,

More information

Development DKMQ Shell Element with Five Degrees of Freedom per Nodal

Development 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 information

COMPUTATIONAL ELASTICITY

COMPUTATIONAL ELASTICITY COMPUTATIONAL ELASTICITY Theory of Elasticity and Finite and Boundary Element Methods Mohammed Ameen Alpha Science International Ltd. Harrow, U.K. Contents Preface Notation vii xi PART A: THEORETICAL ELASTICITY

More information

Back Matter Index The McGraw Hill Companies, 2004

Back Matter Index The McGraw Hill Companies, 2004 INDEX A Absolute viscosity, 294 Active zone, 468 Adjoint, 452 Admissible functions, 132 Air, 294 ALGOR, 12 Amplitude, 389, 391 Amplitude ratio, 396 ANSYS, 12 Applications fluid mechanics, 293 326. See

More information

The Hydraulics of Open Channel Flow: An Introduction

The Hydraulics of Open Channel Flow: An Introduction The Hydraulics of Open Channel Flow: An Introduction Basic principles, sediment motion, hydraulic modelling, design of hydraulic structures Second Edition Hubert Chanson Department of Civil Engineering

More information

BENCHMARK 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 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 information

IMPROVING LATERAL STIFFNESS ESTIMATION IN THE DIAGONAL STRUT MODEL OF INFILLED FRAMES

IMPROVING LATERAL STIFFNESS ESTIMATION IN THE DIAGONAL STRUT MODEL OF INFILLED FRAMES IMPROVING LATERAL STIFFNESS ESTIMATION IN THE DIAGONAL STRUT MODEL OF INFILLED FRAMES I.N. Doudoumis 1 1 Professor, Dept. of Civil Engineering, Aristotle University of Thessaloniki, Thessaloniki, Greece

More information

Introduction to Continuous Systems. Continuous Systems. Strings, Torsional Rods and Beams.

Introduction 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 information

FINITE ELEMENT ANALYSIS OF TAPERED COMPOSITE PLATE GIRDER WITH A NON-LINEAR VARYING WEB DEPTH

FINITE 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 information

My Fifty Years with Finite Elements

My Fifty Years with Finite Elements Robert L. Taylor Department of Civil & Environmental Engineering University of California, Berkeley WCCM8/ECCOMAS 2008 Congress: 20 June - 4 July 2008 Outline: Presentation summarizes: Historical overview

More information

Continuum Mechanics and Theory of Materials

Continuum Mechanics and Theory of Materials Peter Haupt Continuum Mechanics and Theory of Materials Translated from German by Joan A. Kurth Second Edition With 91 Figures, Springer Contents Introduction 1 1 Kinematics 7 1. 1 Material Bodies / 7

More information

Advanced Vibrations. Distributed-Parameter Systems: Exact Solutions (Lecture 10) By: H. Ahmadian

Advanced Vibrations. Distributed-Parameter Systems: Exact Solutions (Lecture 10) By: H. Ahmadian Advanced Vibrations Distributed-Parameter Systems: Exact Solutions (Lecture 10) By: H. Ahmadian ahmadian@iust.ac.ir Distributed-Parameter Systems: Exact Solutions Relation between Discrete and Distributed

More information

Steps in the Finite Element Method. Chung Hua University Department of Mechanical Engineering Dr. Ching I Chen

Steps in the Finite Element Method. Chung Hua University Department of Mechanical Engineering Dr. Ching I Chen Steps in the Finite Element Method Chung Hua University Department of Mechanical Engineering Dr. Ching I Chen General Idea Engineers are interested in evaluating effects such as deformations, stresses,

More information

Moment Area Method. 1) Read

Moment Area Method. 1) Read Moment Area Method Lesson Objectives: 1) Identify the formulation and sign conventions associated with the Moment Area method. 2) Derive the Moment Area method theorems using mechanics and mathematics.

More information

3 2 6 Solve the initial value problem u ( t) 3. a- If A has eigenvalues λ =, λ = 1 and corresponding eigenvectors 1

3 2 6 Solve the initial value problem u ( t) 3. a- If A has eigenvalues λ =, λ = 1 and corresponding eigenvectors 1 Math Problem a- If A has eigenvalues λ =, λ = 1 and corresponding eigenvectors 1 3 6 Solve the initial value problem u ( t) = Au( t) with u (0) =. 3 1 u 1 =, u 1 3 = b- True or false and why 1. if A is

More information