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Barna Szabó
Finite Element Analysis
Читать книгу Finite Element Analysis - Barna Szabó - Страница 1
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Страница 1
Table of Contents
List of Tables
List of Illustrations
Guide
Pages
WILEY SERIES IN COMPUTATIONAL MECHANICS
Finite Element Analysis Method, Verification and Validation
Страница 9
Preface to the second edition
Страница 11
Preface
About the companion website
1 Introduction to the finite element method
1.1 An introductory problem
The choice of basis functions
Summary of the main points
1.2 Generalized formulation
1.2.1 The exact solution
Summary of the main points
1.2.2 The principle of minimum potential energy
1.3 Approximate solutions
1.3.1 The standard polynomial space
Lagrange shape functions
Legendre shape functions
1.3.2 Finite element spaces in one dimension
1.3.3 Computation of the coefficient matrices
Computation of the stiffness matrix
Computation of the Gram matrix
1.3.4 Computation of the right hand side vector
1.3.5 Assembly
1.3.6 Condensation
1.3.7 Enforcement of Dirichlet boundary conditions
1.4 Post‐solution operations
1.4.1 Computation of the quantities of interest
Computation of
uFE
(
x
0
)
Direct computation of
Indirect computation of in node points
Nodal forces
1.5 Estimation of error in energy norm
1.5.1 Regularity
1.5.2 A priori estimation of the rate of convergence
1.5.3 A posteriori estimation of error
Error estimation based on extrapolation
Examples
1.5.4 Error in the extracted QoI
1.6 The choice of discretization in 1D
1.6.1 The exact solution lies in ,
1.6.2 The exact solution lies in ,
1.7 Eigenvalue problems
1.8 Other finite element methods
1.8.1 The mixed method
1.8.2 Nitsche's method
Stabilization
Numerical example
Notes
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