MATLAB Codes for Finite Element Analysis: Solids and Structures ()

Contents......Page 7
1.2 Matrices......Page 10
1.3 Operating with matrices......Page 11
1.5 Matrix functions......Page 12
1.6 Conditionals, if and switch......Page 13
1.7 Loops: for and while......Page 14
1.8 Relations......Page 15
1.9 Scalar functions......Page 16
1.10 Vector functions......Page 17
1.11 Matrix functions......Page 18
1.12 Submatrix......Page 19
1.13 Logical indexing......Page 21
1.14 M-files, scripts and functions......Page 22
1.15.1 2D plots......Page 23
1.15.2 3D plots......Page 24
1.16 Linear algebra......Page 25
2.2 Springs and bars......Page 28
2.3 Equilibrium at nodes......Page 29
2.5 First problem and first MATLAB code......Page 30
2.6 New code using MATLAB structures......Page 37
3.1 A bar element......Page 41
3.2 Numerical integration......Page 44
3.3 An example of isoparametric bar......Page 45
3.4 Problem 2, using MATLAB struct......Page 49
3.5 Problem 3......Page 52
4.2 2D trusses......Page 58
4.3 Stiffness matrix......Page 59
4.5 First 2D truss problem......Page 60
4.6 A second truss problem......Page 65
4.7 An example of 2D truss with spring......Page 70
5.2 A 3D truss problem......Page 75
5.3 A second 3D truss example......Page 79
6.1 Introduction......Page 84
6.2 Bernoulli beam problem......Page 86
6.3 Bernoulli beam with spring......Page 90
7.1 Introduction......Page 93
7.2 An example of 2D frame......Page 95
7.3 Another example of 2D frame......Page 99
8.2 Stiffness matrix and vector of equivalent nodal forces......Page 107
8.3 First 3D frame example......Page 108
8.4 Second 3D frame example......Page 112
9.1 Introduction......Page 117
9.2 A first grid example......Page 120
9.3 A second grid example......Page 123
10.2 Formulation for static analysis......Page 126
10.3 Free vibrations of Timoshenko beams......Page 133
10.4 Buckling analysis of Timoshenko beams......Page 139
11.2 Displacements, strains and stresses......Page 145
11.3 Boundary conditions......Page 146
11.6 Interpolation of displacements......Page 147
11.7 Element energy......Page 148
11.8 Quadrilateral element Q4......Page 149
11.9 Example: plate in traction......Page 151
11.10 Example: beam in bending......Page 154
12.2 The Mindlin plate theory......Page 163
12.2.1 Strains......Page 164
12.3 Finite element discretization......Page 165
12.4 Example: a square Mindlin plate in bending......Page 167
12.5 Free vibrations of Mindlin plates......Page 184
12.6 Buckling analysis of Mindlin plates......Page 194
13.3 Strains......Page 204
13.5 Stresses......Page 206
13.6 Stiffness matrix......Page 208
13.7 Numerical example......Page 209
13.8 Free vibrations of laminated plates......Page 226
References......Page 232
G......Page 234
P......Page 235
V......Page 236