| Preface |
| General problems in solid mechanics and non-linearity / 1： |
| Introduction / 1.1： |
| Small deformation solid mechanics problems / 1.2： |
| Variational forms for non-linear elasticity / 1.3： |
| Weak forms of governing equations / 1.4： |
| Concluding remarks / 1.5： |
| References |
| Galerkin method of approximation - irreducible and mixed forms / 2： |
| Finite element approximation - Galerkin method / 2.1： |
| Numerical integration - quadrature / 2.3： |
| Non-linear transient and steady-state problems / 2.4： |
| Boundary conditions: non-linear problems / 2.5： |
| Mixed or irreducible forms / 2.6： |
| Non-linear quasi-harmonic field problems / 2.7： |
| Typical examples of transient non-linear calculations / 2.8： |
| Solution of non-linear algebraic equations / 2.9： |
| Iterative techniques / 3.1： |
| General remarks - incremental and rate methods / 3.3： |
| Inelastic and non-linear materials / 4： |
| Viscoelasticity - history dependence of deformation / 4.1： |
| Classical time-independent plasticity theory / 4.3： |
| Computation of stress increments / 4.4： |
| Isotropic plasticity models / 4.5： |
| Generalized plasticity / 4.6： |
| Some examples of plastic computation / 4.7： |
| Basic formulation of creep problems / 4.8： |
| Viscoplasticity - a generalization / 4.9： |
| Some special problems of brittle materials / 4.10： |
| Non-uniqueness and localization in elasto-plastic deformations / 4.11： |
| Geometrically non-linear problems - finite deformation / 4.12： |
| Governing equations / 5.1： |
| Variational description for finite deformation / 5.3： |
| Two-dimensional forms / 5.4： |
| A three-field, mixed finite deformation formulation / 5.5： |
| A mixed-enhanced finite deformation formulation / 5.6： |
| Forces dependent on deformation - pressure loads / 5.7： |
| Material constitution for finite deformation / 5.8： |
| Isotropic elasticity / 6.1： |
| Isotropic viscoelasticity / 6.3： |
| Plasticity models / 6.4： |
| Incremental formulations / 6.5： |
| Rate constitutive models / 6.6： |
| Numerical examples / 6.7： |
| Treatment of constraints - contact and tied interfaces / 6.8： |
| Node-node contact: Hertzian contact / 7.1： |
| Tied interfaces / 7.3： |
| Node-surface contact / 7.4： |
| Surface-surface contact / 7.5： |
| Pseudo-rigid and rigid-flexible bodies / 7.6： |
| Pseudo-rigid motions / 8.1： |
| Rigid motions / 8.3： |
| Connecting a rigid body to a flexible body / 8.4： |
| Multibody coupling by joints / 8.5： |
| Discrete element methods / 8.6： |
| Early DEM formulations / 9.1： |
| Contact detection / 9.3： |
| Contact constraints and boundary conditions / 9.4： |
| Block deformability / 9.5： |
| Time integration for discrete element methods / 9.6： |
| Associated discontinuous modelling methodologies / 9.7： |
| Unifying aspects of discrete element methods / 9.8： |
| Structural mechanics problems in one dimension - rods / 9.9： |
| Weak (Galerkin) forms for rods / 10.1： |
| Finite element solution: Euler-Bernoulli rods / 10.4： |
| Finite element solution: Timoshenko rods / 10.5： |
| Forms without rotation parameters / 10.6： |
| Moment resisting frames / 10.7： |
| Plate bending approximation: thin (Kirchhoff) plates and C[subscript 1] continuity requirements / 10.8： |
| The plate problem: thick and thin formulations / 11.1： |
| Rectangular element with corner nodes (12 degrees of freedom) / 11.3： |
| Quadrilateral and parallelogram elements / 11.4： |
| Triangular element with corner nodes (9 degrees of freedom) / 11.5： |
| Triangular element of the simplest form (6 degrees of freedom) / 11.6： |
| The patch test - an analytical requirement / 11.7： |
| General remarks / 11.8： |
| Singular shape functions for the simple triangular element / 11.10： |
| An 18 degree-of-freedom triangular element with conforming shape functions / 11.11： |
| Compatible quadrilateral elements / 11.12： |
| Quasi-conforming elements / 11.13： |
| Hermitian rectangle shape function / 11.14： |
| The 21 and 18 degree-of-freedom triangle / 11.15： |
| Mixed formulations - general remarks / 11.16： |
| Hybrid plate elements / 11.17： |
| Discrete Kirchhoff constraints / 11.18： |
| Rotation-free elements / 11.19： |
| Inelastic material behaviour / 11.20： |
| Concluding remarks - which elements? / 11.21： |
| 'Thick' Reissner-Mindlin plates - irreducible and mixed formulations / 12： |
| The irreducible formulation - reduced integration / 12.1： |
| Mixed formulation for thick plates / 12.3： |
| The patch test for plate bending elements / 12.4： |
| Elements with discrete collocation constraints / 12.5： |
| Elements with rotational bubble or enhanced modes / 12.6： |
| Linked interpolation - an improvement of accuracy / 12.7： |
| Discrete 'exact' thin plate limit / 12.8： |
| Performance of various 'thick' plate elements - limitations of thin plate theory / 12.9： |
| Concluding remarks - adaptive refinement / 12.10： |
| Shells as an assembly of flat elements / 13： |
| Stiffness of a plane element in local coordinates / 13.1： |
| Transformation to global coordinates and assembly of elements / 13.3： |
| Local direction cosines / 13.4： |
| 'Drilling' rotational stiffness - 6 degree-of-freedom assembly / 13.5： |
| Elements with mid-side slope connections only / 13.6： |
| Choice of element / 13.7： |
| Practical examples / 13.8： |
| Curved rods and axisymmetric shells / 14： |
| Straight element / 14.1： |
| Curved elements / 14.3： |
| Independent slope-displacement interpolation with penalty functions (thick or thin shell formulations) / 14.4： |
| Shells as a special case of three-dimensional analysis - Reissner-Mindlin assumptions / 15： |
| Shell element with displacement and rotation parameters / 15.1： |
| Special case of axisymmetric, curved, thick shells / 15.3： |
| Special case of thick plates / 15.4： |
| Convergence / 15.5： |
| Inelastic behaviour / 15.6： |
| Some shell examples / 15.7： |
| Semi-analytical finite element processes - use of orthogonal functions and 'finite strip' methods / 15.8： |
| Prismatic bar / 16.1： |
| Thin membrane box structures / 16.3： |
| Plates and boxes with flexure / 16.4： |
| Axisymmetric solids with non-symmetrical load / 16.5： |
| Axisymmetric shells with non-symmetrical load / 16.6： |
| Non-linear structural problems - large displacement and instability / 16.7： |
| Large displacement theory of beams / 17.1： |
| Elastic stability - energy interpretation / 17.3： |
| Large displacement theory of thick plates / 17.4： |
| Large displacement theory of thin plates / 17.5： |
| Solution of large deflection problems / 17.6： |
| Shells / 17.7： |
| Multiscale modelling / 17.8： |
| Asymptotic analysis / 18.1： |
| Statement of the problem and assumptions / 18.3： |
| Formalism of the homogenization procedure / 18.4： |
| Global solution / 18.5： |
| Local approximation of the stress vector / 18.6： |
| Finite element analysis applied to the local problem / 18.7： |
| The non-linear case and bridging over several scales / 18.8： |
| Asymptotic homogenization at three levels: micro, meso and macro / 18.9： |
| Recovery of the micro description of the variables of the problem / 18.10： |
| Material characteristics and homogenization results / 18.11： |
| Multilevel procedures which use homogenization as an ingredient / 18.12： |
| General first-order and second-order procedures / 18.13： |
| Discrete-to-continuum linkage / 18.14： |
| Local analysis of a unit cell / 18.15： |
| Homogenization procedure - definition of successive yield surfaces / 18.16： |
| Numerically developed global self-consistent elastic-plastic constitutive law / 18.17： |
| Global solution and stress-recovery procedure / 18.18： |
| Computer procedures for finite element analysis / 18.19： |
| Solution of non-linear problems / 19.1： |
| Eigensolutions / 19.3： |
| Restart option / 19.4： |
| Isoparametric finite element approximations / 19.5： |
| Invariants of second-order tensors / Appendix B： |
| Author index |
| Subject index |
| Preface |
| General problems in solid mechanics and non-linearity / 1： |
| Introduction / 1.1： |
図書
