The finite element method for solid and structural mechanics - Zienkiewicz, O. C. (Elsevier Butterworth-Heinemann, 2005)
Includes bibliographical references and indexes
Cover -- The Finite Element Method for Solid and Structural Mechanics Sixth edition -- Contents -- Preface -- 1. General problems in solid mechanics and non-linearity -- 1.1 Introduction -- 1.2 Small deformation solid mechanics problems -- 1.3 Variational forms for non-linear elasticity -- 1.4 Weak forms of governing equations -- 1.5 Concluding remarks -- References -- 2. Galerkin method of approximation -- irreducible and mixed forms -- 2.1 Introduction -- 2.2 Finite element approximation -- Galerkin method -- 2.3 Numerical integration -- quadrature -- 2.4 Non-linear transient and steady-state problems -- 2.5 Boundary conditions: non-linear problems -- 2.6 Mixed or irreducible forms -- 2.7 Non-linear quasi-harmonic field problems -- 2.8 Typical examples of transient non-linear calculations -- 2.9 Concluding remarks -- References -- 3. Solution of non-linear algebraic equations -- 3.1 Introduction -- 3.2 Iterative techniques -- 3.3 General remarks -- incremental and rate methods --
- References -- 4. Inelastic and non-linear materials -- 4.1 Introduction -- 4.2 Viscoelasticity -- history dependence of deformation -- 4.3 Classical time-independent plasticity theory -- 4.4 Computation of stress increments -- 4.5 Isotropic plasticity models -- 4.6 Generalized plasticity -- 4.7 Some examples of plastic computation -- 4.8 Basic formulation of creep problems -- 4.9 Viscoplasticity -- a generalization -- 4.10 Some special problems of brittle materials -- 4.11 Non-uniqueness and localization in elasto-plastic deformations -- 4.12 Non-linear quasi-harmonic field problems -- 4.13 Concluding remarks -- References -- 5. Geometrically non-linear problems -- finite deformation -- 5.1 Introduction -- 5.2 Governing equations -- 5.3 Variational description for finite deformation -- 5.4 Two-dimensional forms -- 5.5 A three-field, mixed finite deformation formulation -- 5.6 A mixed-enhanced finite deformation formulation -- 5.7 Forces dependent on deformation -- pressure loads --
- 5.8 Concluding remarks -- References -- 6. Material constitution for finite deformation -- 6.1 Introduction -- 6.2 Isotropic elasticity -- 6.3 Isotropic viscoelasticity -- 6.4 Plasticity models -- 6.5 Incremental formulations -- 6.6 Rate constitutive models -- 6.7 Numerical examples -- 6.8 Concluding remarks -- References -- 7. Treatment of constraints -- contact and tied interfaces -- 7.1 Introduction -- 7.2 Node-node contact: Hertzian contact -- 7.3 Tied interfaces -- 7.4 Node-surface contact -- 7.5 Surface-surface contact -- 7.6 Numerical examples -- 7.7 Concluding remarks -- References -- 8. Pseudo-rigid and rigid-flexible bodies -- 8.1 Introduction -- 8.2 Pseudo-rigid motions -- 8.3 Rigid motions -- 8.4 Connecting a rigid bo