Cover
Title Page
Copyright
Contents
Preface to the second edition
Preface to the first edition
Preface
About the companion website
Chapter 1 Introduction to the finite element method
1.1 An introductory problem
1.2 Generalized formulation
1.2.1 The exact solution
1.2.2 The principle of minimum potential energy
1.3 Approximate solutions
1.3.1 The standard polynomial space
1.3.2 Finite element spaces in one dimension
1.3.3 Computation of the coefficient matrices
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
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
1.5.4 Error in the extracted QoI
1.6 The choice of discretization in 1D
1.6.1 The exact solution lies in Hk(I), k−1&lt
p
1.6.2 The exact solution lies in Hk(I), k−1≤p
1.7 Eigenvalue problems
1.8 Other finite element methods
1.8.1 The mixed method
1.8.2 Nitsche's method
Chapter 2 Boundary value problems
2.1 Notation
2.2 The scalar elliptic boundary value problem
2.2.1 Generalized formulation
2.2.2 Continuity
2.3 Heat conduction
2.3.1 The differential equation
2.3.2 Boundary and initial conditions
2.3.3 Boundary conditions of convenience
2.3.4 Dimensional reduction
2.4 Equations of linear elasticity - strong form
2.4.1 The Navier equations
2.4.2 Boundary and initial conditions
2.4.3 Symmetry, antisymmetry and periodicity
2.4.4 Dimensional reduction in linear elasticity
2.4.5 Incompressible elastic materials
2.5 Stokes flow
2.6 Generalized formulation of problems of linear elasticity. H.3.3 Combined (Mode I and Mode II) loading
H.3.4 Computation by the stiffness derivative method
Appendix I Fundamentals of data analysis
I.1 Statistical foundations
I.2 Test data
I.3 Statistical models
I.4 Ranking
I.5 Confidence intervals
Appendix J Estimation of fastener forces in structural connections
Appendix K Useful algorithms in solid mechanics
K.1 The traction vector
K.2 Transformation of vectors
K.3 Transformation of stresses
K.4 Principal stresses
K.5 The von Mises stress
K.6 Statically equivalent forces and moments
K.6.1 Technical formulas for stress
Bibliography
Index
EULA

Finite Element Analysis: Method, Verification and Validation, Second Edition comprehensively covers the theoretical foundation of the of the finite element method with particular focus on the fundamentals of verification, validation and uncertainty quantification. It illustrates the techniques and procedures of quality assurance in numerical simulation through examples and exercises and describes the technical requirements for the formulation and application of design rules. Finite Element Analysis: Method, Verification and Validation, Second Edition bridges the gap between theory and numerical results in a unique and accessible way and is accompanied by a website hosting a solutions manual, powerpoint slides for instructors and a link to finite element software.