Preface to Volume 2 1. General problems in solid mecbanics and non-linearity 1.1 Introduction 1.2 Small deformation nondinear solid mechanics problems 1.3 Non-linear quasi harmonic field problems 1.4 Some typical examples of tr msient non-linear calculations 1.5 Concluding remarks References 2 Solution of non-linear algebraie equations 2.1 Introduction 2.2 Iterafive techniques References 3 Inelastic and non-linear materials 3.1 Introduction 3.2 Viscoelasticity history dependence ofdeforma on 3.3 Classical timedndependent plasticity theory 3.4 Computation of stress increments 3.5 lsotropie plasticity models 3.6 Generalized plasticity non-associative case 3.7 Some examples of plastic computation 3.8 Basic formulafion of creep problems 3.9 Viscoplasticity a generalization 3.10 Some special problems of brit tie materials 3.11 Non-uniqueness and localization in elast o-plastic deformations 3.12 Adaptive refinement and localization (slip line) capture 3.13 Non-linear q uasi-hannonic field problems References 4. Plate bending approximation: thin (Kircbbofi) plates and c1 continuity requirements 4.1 Introduction 4.2 The piale problem: thick and thin formulations 4.3 Rectangular element with corner nodes (12 degrees of freedom) 4.4 Quadrilateral and parallelogram elements 4.5 Triangular element with corner nodes (9 degrees of freedom) 4.6 Triangular element of the simplest form (6 degrees of freedom) 4.7 The patch test an analytical requirement 4.8 Numerical examples 4.9 General remarks 4.10 Singular shape functions for the simple triangular element 4.11 An 18 degree of-freedom triangular element with conforming shape functions 4.12 Compatible quadrdateral element 4.13 Quasi-confoming elements 4.14 Hermitian rectangle shape function 4.15 The 21 and 18 degree-of-freedom triangle 4.16 Mixed forulations - general remarks 4.17 Hybrid plate elements 4.18 Discrte Kirchhoffconstraints 4.20 Inelastic material behaviour 4.21 Concluding remarks - which elements? References 5 'Thick' Reissner Mindlin plates - irreducible and mixed formuladons 5.1 Introduction 5.2 The irreducible formutation reduced integration 5.3 Mixed formulation for thick plates 5.4 The patch test for plate bending elements 5.5 Elements with discrete collocation constraints 5.6 Elements wilh rotational bubble or enhanced modes 5.7 Linked interpolation an improvement of accuracy 5.8 Discrete "exact' thin plate limit 5.9 Performance of various 'thick' plate elements lindtations of thin plate theory 5.10 Forms without rotation parameters 5.11 Inelastic material behaviour 5.12 Concluding remarks adaptive refinement References 6. Shegs as an assembly of flat elements 6.1 Introduction 6.2 Stiffness of a plane element in local coordinates 6.3 Transformation to globM coordinates and assembly of elements 6.4 Local direction cosines 6.5 'Drilling' rotational stiffness 6 degree of-freedom assembly 6.6 Elements with mid-side slope connections only 6.7 Choice of element 6.8 Practical examples References 7. Axisymmetric shells 8. Shells as a special case of three-dimensional analysis-Reissner-Mindlin assumptions 9. Semi-analytical finite element processes-usr of orthogonal functions and 'finite strip'methods 10. Geometrically non-linear problems-finite deformation 11. Non-linear stuctural problems-large displacement and instability 12. Pseudo-rigid and rigid-flexible bodies 13. Computr procedures for finite element analysis Appendix A:Invariants of second-order tensors Author index Subject index
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