# MATLAB Codes for Finite Element Analysis: Solids and Structures

Springer Science & Business Media, Nov 6, 2008 - Technology & Engineering - 235 pages
This book intend to supply readers with some MATLAB codes for ?nite element analysis of solids and structures. After a short introduction to MATLAB, the book illustrates the ?nite element implementation of some problems by simple scripts and functions. The following problems are discussed: • Discrete systems, such as springs and bars • Beams and frames in bending in 2D and 3D • Plane stress problems • Plates in bending • Free vibration of Timoshenko beams and Mindlin plates, including laminated composites • Buckling of Timoshenko beams and Mindlin plates The book does not intends to give a deep insight into the ?nite element details, just the basic equations so that the user can modify the codes. The book was prepared for undergraduate science and engineering students, although it may be useful for graduate students. TheMATLABcodesofthisbookareincludedinthedisk.Readersarewelcomed to use them freely. The author does not guarantee that the codes are error-free, although a major e?ort was taken to verify all of them. Users should use MATLAB 7.0 or greater when running these codes. Any suggestions or corrections are welcomed by an email to ferreira@fe.up.pt.

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### Contents

 Short introduction to MATLAB 1 13 Operating with matrices 2 14 Statements 3 16 Conditionals if and switch 4 for and while 5 18 Relations 6 19 Scalar functions 7 110 Vector functions 8
 53 A second 3D truss example 73 Bernoulli beams 78 62 Bernoulli beam problem 81 63 Bernoulli beam with spring 85 2D frames 89 73 Another example of 2D frame 95 Analysis of grids 113 92 A ﬁrst grid example 116

 111 Matrix functions 9 112 Submatrix 10 113 Logical indexing 12 114 Mﬁles scripts and functions 13 1151 2D plots 14 1152 3D plots 15 116 Linear algebra 16 Discrete systems 19 23 Equilibrium at nodes 20 24 Some basic steps 21 Analysis of bars 33 34 Problem 2 using MATLAB struct 41 35 Problem 3 44 Analysis of 2D trusses 50 43 Stiffness matrix 52 44 Stresses at the element 53 Trusses in 3D space 69
 93 A second grid example 119 Analysis of Timoshenko beams 122 Plane stress 143 113 Boundary conditions 144 114 Potential energy 145 117 Element energy 146 118 Quadrilateral element Q4 147 plate in traction 149 beam in bending 152 Analysis of Mindlin plates 161 1221 Strains 162 1222 Stresses 163 a square Mindlin plate in bending 165 Laminated plates 202 References 231 Index 233 Copyright