Page 204 - Using ANSYS for Finite Element Analysis A Tutorial for Engineers

Index • 191
discretization error, 50–51 L
history of, 5 linear algebraic equations
modeling error, 49–50 Cramer’s rule, 22–23
numerical error, 51–52 Gaussian elimination, 23–26
finite element method (FEM) inversion, 23
bar element formulation, linear behavior, 9–10
31–33 linear material properties, 59–60
description, 1 linear vs. nonlinear static analysis,
element characteristic matrix, 54
27–28 load step options, 63
examples, 34–48
FEA, 6–8 (see also finite element M
analysis (FEA)) material properties, 59
mathematical model, 1–3, 5–6 mathematical model, 1–3, 5–6
numerical methods, 4 matrix algebra, 15–17
physical, 6 mechanical structure (thermal
spring element equations, analysis)
28–31 ANSYS solution, 162–168
steps of, 26–27 loads and material properties,
structural analysis (see structural 161
analysis of FEM) modal analysis, 10
types, 27 modeling, 48–49
force / flexibility method, 26 modeling error, 49–50
fracture mechanics, 12 multi-physics application, 14
multiplication of a matrix by a
G scalar, 15
Galerkin method, 28 multiplication of two matrices, 15
Gaussian elimination, 23–26
geometric modeling N
solid model, 68–69 nonlinear analysis, 11
steps in, 65–66 nonlinear behavior, 9–10
3D, 79–89 nonlinear material properties,
2D, 69–78 60–61
using CAD system, 66–68 nonstructural application, 14
numerical error, 51–52
H numerical methods, 4
harmonic analysis, 10
heat transfer analysis, 9 O
one dimension elasticity equation,
I 20
identity matrix, 16
integrating a matrix, 16 P
inverse of a matrix, 16 physical FEM, 6
inversion, 23 plane strain elasticity equation, 21