MATLAB Codes for Finite Element Analysis: Solids and Structures

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Springer Science & Business Media, Nov 6, 2008 - Technology & Engineering - 235 pages
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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

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

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2D frame 2D truss A.J.M. Ferreira antonio ferreira 2008 boundary conditions buckling CCCF clear memory clear codes for Finite conditions and solution coordinates and connectivities cycle for element cycle for Gauss defined deformed shape degrees of freedom derivatives shapeFunction,naturalDerivatives]=shapeFunctionQ4(xi,eta derivatives w.r.t. x,y displacement vector element degrees elementDof elementNodes eta=GaussPoint(2 finite element Finite Element Analysis first fixedNodeW force vector force=zeros(GDof,1 free vibrations freedom Dof freedom GDof=3*numberNodes functions and derivatives Gauss point end Gauss quadrature GDof GDof,prescribedDof GDof=2*numberNodes global number illustrated in figure indice=elementNodes(e inverse of Jacobian Jacobian matrix Jacobian(nodeCoordinates(indice,:),naturalDerivatives length of bar MATLAB codes modulus of elasticity natural frequencies ndof=length(indice number of degrees number of elements numberElements numberNodes obtained output displacements/reactions outputDisplacementsReactions(displacements,stiffness plate with h/a Q4 elements shape functions shear modulus simply-supported Solid Mechanics Solids and Structures solution displacements=solution(GDof,prescribedDof,stiffness,force Springer Science+Business Media stiffness stiffness(elementDof,elementDof strain energy stresses system stiffness matrix Timoshenko beam w.r.t. x,y Jacob,invJacobian,XYderivatives xi=GaussPoint(1 xx=nodeCoordinates(:,1 XYderivatives(:,2 yy=nodeCoordinates(:,2

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