# The Finite Element Method Using MATLAB, Second Edition

CRC Press, Jul 28, 2000 - Technology & Engineering - 624 pages
Expanded to include a broader range of problems than the bestselling first edition, Finite Element Method Using MATLAB: Second Edition presents finite element approximation concepts, formulation, and programming in a format that effectively streamlines the learning process. It is written from a general engineering and mathematical perspective rather than that of a solid/structural mechanics basis.

What's new in the Second Edition?

Each chapter in the Second Edition now includes an overview that outlines the contents and purpose of each chapter. The authors have also added a new chapter of special topics in applications, including cracks, semi-infinite and infinite domains, buckling, and thermal stress. They discuss three different linearization techniques to solve nonlinear differential equations. Also included are new sections on shell formulations and MATLAB programs. These enhancements increase the book's already significant value both as a self-study text and a reference for practicing engineers and scientists.

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this is the needed one for programing
That is the first to be read

### Contents

 INTRODUCTION TO MATLAB 1 12 Overview of the Book 2 14 Vector and Matrix Manipulations 3 15 Matrix Functions 4 16 Data Analysis Functions 10 17 Tools for Polynomials 12 18 Making Complex Numbers 15 110 Solving Differential Equations 17
 85 Hybrid Beam Element 255 86 Composite Beams 259 87 TwoDimensional Frame Element 262 88 ThreeDimensional Frame Element 265 89 MATLAB Application to Static Analysis 268 810 MATLAB Application to Eigenvalue Analysis 283 811 MATLAB Application to Transient Analysis 287 812 MATLAB Application to Modal Analysis of Undamped System 292

 111 Loop and Logical Statements 18 112 Writing Function Subroutines 20 113 File Manipulation 22 114 Basic InputOutput Functions 23 115 Plotting Tools 24 APPROXIMATION TECHNIQUES 31 22 Weak Formulation 34 23 Piecewise Continuous Trial Function 35 24 Galerkins Finite Element Formulation 37 25 Variational Method 42 27 RayleighRitz Finite Element Method 43 Problems 46 FINITE ELEMENT PROGRAMMING 51 32 Input Data 52 33 Assembly of Element Matrices and Vectors 54 35 Example Programs 56 Problems 70 DIRECT APPROACH WITH SPRING SYSTEM 71 42 Axial Member 74 43 Torsional Member 76 44 Other Systems 78 Problems 81 LAPLACES AND POISSONS EQUATIONS 85 52 Linear Triangular Element 88 53 Bilinear Rectangular Element 92 54 Boundary Integral 94 55 Transient Analysis 98 56 Time Integration Technique 100 57 Axisymmetric Analysis 103 58 ThreeDimensional Analysis 105 59 MATLAB Application to 2D Steady State Analysis 109 510 MATLAB Application to Axisymmetric Analysis 121 511 MATLAB Application to Transient Analysis 126 512 MATLAB Application to 3D Steady State Analysis 150 Problems 155 ISOPARAMETRIC ELEMENTS 159 62 Quadrilateral Elements 163 63 Triangular Elements 171 64 Gauss Quadrature 172 65 MATLAB Application to Gauss Quadrature 179 66 MATLAB Application to Laplaces Equation 186 Problems 195 TRUSS STRUCTURES 199 72 Plane Truss 201 73 Space Truss 205 74 MATLAB Application to Static Analysis 206 75 MATLAB Application to Eigenvalue Analysis 218 76 MATLAB Application to Transient Analysis 226 Problems 234 BEAM AND FRAME STRUCTURES 237 82 Timoshenko Beam 244 83 Beam Elements with Only Displacement Degrees of Freedom 248 84 Mixed Beam Element 252
 813 MATLAB Application to Modal Analysis of Damped System 299 814 MATLAB Application to Frequency Response Analysis 302 Problems 307 ELASTICITY PROBLEM 311 92 Force Vector 315 93 Energy Method 317 94 ThreeDimensional Solid 319 95 Axisymmetric Solid 322 96 Dynamic Analysis 324 97 Thermal Stress 325 98 MATLAB Application to 2D Stress Analysis 327 99 MATLAB Application to Axisymmetric Analysis 339 910 MATLAB Application to 3D Stress Analysis 351 Problems 361 PLATE AND SHELL STRUCTURES 365 102 Classical Plate Bending Element 368 103 Shear Deformable Plate Element 370 104 Plate Element With Displacement Degrees of Freedom 373 105 Mixed Plate Element 377 106 Hybrid Plate Element 383 107 Shell Made of Inplane and Bending Elements 386 108 Shell Degenerated from 3D Solid 389 109 MATLAB Application to Plates 394 1010 MATLAB Application to Shells 401 Problems 424 CONTROL OF FLEXIBLE STRUCTURES 427 112 Stability Theory 429 113 Stability of Multiple Degrees of Freedom Systems 432 114 Analysis of a Second Order System 436 115 State Space Form Description 441 116 Transfer Function Analysis 451 117 Control Law Design for State Space Systems 461 118 Linear Quadratic Regulator 472 119 Modal Control for Second Order Systems 482 1110 Dynamic Observer 485 1111 Compensator Design 490 1112 Output Feedback Design by Using Collocated SensorActuator Discrete Multiple Degrees of Freedom System 494 Problems 509 SPECIAL TOPICS 513 122 QuarterPoint Singular Elements 519 123 Moving Singular Elements 522 124 SemiInfinite Element 528 125 Thermal Stress in Layered Beams 531 126 Buckling Analysis 534 127 Nonlinear Analysis 537 128 MATLAB Application to Buckling Problem 539 129 MATLAB Application to Nonlinear Problem 541 REFERENCES 557 FEM MATLAB FUNCTION FILES 563 EXAMPLES OF PRE AND POSTPROCESSOR 591 INDEX 599 Copyright