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This is the key text and reference for engineers, researchers and senior students dealing with the analysis and modelling of structures - from large civil engineering projects such as dams, to aircraft structures, through to small engineered components. Covering small and large deformation behaviour of solids and structures, it is an essential book for engineers and mathematicians. The new edition is a complete solids and structures text and reference in its own right and forms part of the world-renowned Finite Element Method series by Zienkiewicz and Taylor.

New material in this edition includes separate coverage of solid continua and structural theories of rods, plates and shells; extended coverage of plasticity (isotropic and anisotropic); node-to-surface and 'mortar' method treatments; problems involving solids and rigid and pseudo-rigid bodies; and multi-scale modelling.

Tabla de contenidos provista por Syndetics

• Preface(p. xiii)
• 1 General problems in solid mechanics and non-linearity(p. 1)
• 1.1 Introduction(p. 1)
• 1.2 Small deformation solid mechanics problems(p. 4)
• 1.3 Variational forms for non-linear elasticity(p. 12)
• 1.4 Weak forms of governing equations(p. 14)
• 1.5 Concluding remarks(p. 15)
• References(p. 15)
• 2 Galerkin method of approximation - irreducible and mixed forms(p. 17)
• 2.1 Introduction(p. 17)
• 2.2 Finite element approximation - Galerkin method(p. 17)
• 2.3 Numerical integration - quadrature(p. 22)
• 2.4 Non-linear transient and steady-state problems(p. 24)
• 2.5 Boundary conditions: non-linear problems(p. 28)
• 2.6 Mixed or irreducible forms(p. 33)
• 2.7 Non-linear quasi-harmonic field problems(p. 37)
• 2.8 Typical examples of transient non-linear calculations(p. 38)
• 2.9 Concluding remarks(p. 43)
• References(p. 44)
• 3 Solution of non-linear algebraic equations(p. 46)
• 3.1 Introduction(p. 46)
• 3.2 Iterative techniques(p. 47)
• 3.3 General remarks - incremental and rate methods(p. 58)
• References(p. 60)
• 4 Inelastic and non-linear materials(p. 62)
• 4.1 Introduction(p. 62)
• 4.2 Viscoelasticity - history dependence of deformation(p. 63)
• 4.3 Classical time-independent plasticity theory(p. 72)
• 4.4 Computation of stress increments(p. 80)
• 4.5 Isotropic plasticity models(p. 85)
• 4.6 Generalized plasticity(p. 92)
• 4.7 Some examples of plastic computation(p. 95)
• 4.8 Basic formulation of creep problems(p. 100)
• 4.9 Viscoplasticity - a generalization(p. 102)
• 4.10 Some special problems of brittle materials(p. 107)
• 4.11 Non-uniqueness and localization in elasto-plastic deformations(p. 112)
• 4.12 Non-linear quasi-harmonic field problems(p. 116)
• 4.13 Concluding remarks(p. 118)
• References(p. 120)
• 5 Geometrically non-linear problems - finite deformation(p. 127)
• 5.1 Introduction(p. 127)
• 5.2 Governing equations(p. 128)
• 5.3 Variational description for finite deformation(p. 135)
• 5.4 Two-dimensional forms(p. 143)
• 5.5 A three-field, mixed finite deformation formulation(p. 145)
• 5.6 A mixed-enhanced finite deformation formulation(p. 150)
• 5.7 Forces dependent on deformation - pressure loads(p. 154)
• 5.8 Concluding remarks(p. 155)
• References(p. 156)
• 6 Material constitution for finite deformation(p. 158)
• 6.1 Introduction(p. 158)
• 6.2 Isotropic elasticity(p. 158)
• 6.3 Isotropic viscoelasticity(p. 172)
• 6.4 Plasticity models(p. 173)
• 6.5 Incremental formulations(p. 174)
• 6.6 Rate constitutive models(p. 176)
• 6.7 Numerical examples(p. 178)
• 6.8 Concluding remarks(p. 185)
• References(p. 189)
• 7 Treatment of constraints - contact and tied interfaces(p. 191)
• 7.1 Introduction(p. 191)
• 7.2 Node-node contact: Hertzian contact(p. 193)
• 7.3 Tied interfaces(p. 197)
• 7.4 Node-surface contact(p. 200)
• 7.5 Surface-surface contact(p. 218)
• 7.6 Numerical examples(p. 219)
• 7.7 Concluding remarks(p. 224)
• References(p. 224)
• 8 Pseudo-rigid and rigid-flexible bodies(p. 228)
• 8.1 Introduction(p. 228)
• 8.2 Pseudo-rigid motions(p. 228)
• 8.3 Rigid motions(p. 230)
• 8.4 Connecting a rigid body to a flexible body(p. 234)
• 8.5 Multibody coupling by joints(p. 237)
• 8.6 Numerical examples(p. 240)
• References(p. 242)
• 9 Discrete element methods(p. 245)
• 9.1 Introduction(p. 245)
• 9.2 Early DEM formulations(p. 247)
• 9.3 Contact detection(p. 250)
• 9.4 Contact constraints and boundary conditions(p. 256)
• 9.5 Block deformability(p. 260)
• 9.6 Time integration for discrete element methods(p. 267)
• 9.7 Associated discontinuous modelling methodologies(p. 270)
• 9.8 Unifying aspects of discrete element methods(p. 271)
• 9.9 Concluding remarks(p. 272)
• References(p. 273)
• 10 Structural mechanics problems in one dimension - rods(p. 278)
• 10.1 Introduction(p. 278)
• 10.2 Governing equations(p. 279)
• 10.3 Weak (Galerkin) forms for rods(p. 285)
• 10.4 Finite element solution: Euler-Bernoulli rods(p. 290)
• 10.5 Finite element solution: Timoshenko rods(p. 305)
• 10.6 Forms without rotation parameters(p. 317)
• 10.7 Moment resisting frames(p. 319)
• 10.8 Concluding remarks(p. 320)
• References(p. 320)
• 11 Plate bending approximation: thin (Kirchhoff) plates and C[subscript 1] continuity requirements(p. 323)
• 11.1 Introduction(p. 323)
• 11.2 The plate problem: thick and thin formulations(p. 325)
• 11.3 Rectangular element with corner nodes (12 degrees of freedom)(p. 336)
• 11.4 Quadrilateral and parallelogram elements(p. 340)
• 11.5 Triangular element with corner nodes (9 degrees of freedom)(p. 340)
• 11.6 Triangular element of the simplest form (6 degrees of freedom)(p. 345)
• 11.7 The patch test - an analytical requirement(p. 346)
• 11.8 Numerical examples(p. 348)
• 11.9 General remarks(p. 357)
• 11.10 Singular shape functions for the simple triangular element(p. 357)
• 11.11 An 18 degree-of-freedom triangular element with conforming shape functions(p. 360)
• 11.12 Compatible quadrilateral elements(p. 361)
• 11.13 Quasi-conforming elements(p. 362)
• 11.14 Hermitian rectangle shape function(p. 363)
• 11.15 The 21 and 18 degree-of-freedom triangle(p. 364)
• 11.16 Mixed formulations - general remarks(p. 366)
• 11.17 Hybrid plate elements(p. 368)
• 11.18 Discrete Kirchhoff constraints(p. 369)
• 11.19 Rotation-free elements(p. 371)
• 11.20 Inelastic material behaviour(p. 374)
• 11.21 Concluding remarks - which elements?(p. 376)
• References(p. 376)
• 12 'Thick' Reissner-Mindlin plates - irreducible and mixed formulations(p. 382)
• 12.1 Introduction(p. 382)
• 12.2 The irreducible formulation - reduced integration(p. 385)
• 12.3 Mixed formulation for thick plates(p. 390)
• 12.4 The patch test for plate bending elements(p. 392)
• 12.5 Elements with discrete collocation constraints(p. 397)
• 12.6 Elements with rotational bubble or enhanced modes(p. 405)
• 12.7 Linked interpolation - an improvement of accuracy(p. 408)
• 12.8 Discrete 'exact' thin plate limit(p. 413)
• 12.9 Performance of various 'thick' plate elements - limitations of thin plate theory(p. 415)
• 12.10 Inelastic material behaviour(p. 419)
• 12.11 Concluding remarks - adaptive refinement(p. 420)
• References(p. 421)
• 13 Shells as an assembly of flat elements(p. 426)
• 13.1 Introduction(p. 426)
• 13.2 Stiffness of a plane element in local coordinates(p. 428)
• 13.3 Transformation to global coordinates and assembly of elements(p. 429)
• 13.4 Local direction cosines(p. 431)
• 13.5 'Drilling' rotational stiffness - 6 degree-of-freedom assembly(p. 435)
• 13.6 Elements with mid-side slope connections only(p. 440)
• 13.7 Choice of element(p. 440)
• 13.8 Practical examples(p. 441)
• References(p. 450)
• 14 Curved rods and axisymmetric shells(p. 454)
• 14.1 Introduction(p. 454)
• 14.2 Straight element(p. 454)
• 14.3 Curved elements(p. 461)
• 14.4 Independent slope-displacement interpolation with penalty functions (thick or thin shell formulations)(p. 468)
• References(p. 473)
• 15 Shells as a special case of three-dimensional analysis - Reissner-Mindlin assumptions(p. 475)
• 15.1 Introduction(p. 475)
• 15.2 Shell element with displacement and rotation parameters(p. 475)
• 15.3 Special case of axisymmetric, curved, thick shells(p. 484)
• 15.4 Special case of thick plates(p. 487)
• 15.5 Convergence(p. 487)
• 15.6 Inelastic behaviour(p. 488)
• 15.7 Some shell examples(p. 488)
• 15.8 Concluding remarks(p. 493)
• References(p. 495)
• 16 Semi-analytical finite element processes - use of orthogonal functions and 'finite strip' methods(p. 498)
• 16.1 Introduction(p. 498)
• 16.2 Prismatic bar(p. 501)
• 16.3 Thin membrane box structures(p. 504)
• 16.4 Plates and boxes with flexure(p. 505)
• 16.5 Axisymmetric solids with non-symmetrical load(p. 507)
• 16.6 Axisymmetric shells with non-symmetrical load(p. 510)
• 16.7 Concluding remarks(p. 514)
• References(p. 515)
• 17 Non-linear structural problems - large displacement and instability(p. 517)
• 17.1 Introduction(p. 517)
• 17.2 Large displacement theory of beams(p. 517)
• 17.3 Elastic stability - energy interpretation(p. 523)
• 17.4 Large displacement theory of thick plates(p. 526)
• 17.5 Large displacement theory of thin plates(p. 532)
• 17.6 Solution of large deflection problems(p. 534)
• 17.7 Shells(p. 537)
• 17.8 Concluding remarks(p. 542)
• References(p. 543)
• 18 Multiscale modelling(p. 547)
• 18.1 Introduction(p. 547)
• 18.2 Asymptotic analysis(p. 549)
• 18.3 Statement of the problem and assumptions(p. 550)
• 18.4 Formalism of the homogenization procedure(p. 552)
• 18.5 Global solution(p. 553)
• 18.6 Local approximation of the stress vector(p. 554)
• 18.7 Finite element analysis applied to the local problem(p. 555)
• 18.8 The non-linear case and bridging over several scales(p. 560)
• 18.9 Asymptotic homogenization at three levels: micro, meso and macro(p. 561)
• 18.10 Recovery of the micro description of the variables of the problem(p. 562)
• 18.11 Material characteristics and homogenization results(p. 565)
• 18.12 Multilevel procedures which use homogenization as an ingredient(p. 567)
• 18.13 General first-order and second-order procedures(p. 570)
• 18.14 Discrete-to-continuum linkage(p. 572)
• 18.15 Local analysis of a unit cell(p. 578)
• 18.16 Homogenization procedure - definition of successive yield surfaces(p. 578)
• 18.17 Numerically developed global self-consistent elastic-plastic constitutive law(p. 580)
• 18.18 Global solution and stress-recovery procedure(p. 581)
• 18.19 Concluding remarks(p. 586)
• References(p. 587)
• 19 Computer procedures for finite element analysis(p. 590)
• 19.1 Introduction(p. 590)
• 19.2 Solution of non-linear problems(p. 591)
• 19.3 Eigensolutions(p. 592)
• 19.4 Restart option(p. 594)
• 19.5 Concluding remarks(p. 595)
• References(p. 595)
• Appendix A Isoparametric finite element approximations(p. 597)
• Appendix B Invariants of second-order tensors(p. 604)
• Author index(p. 609)
• Subject index(p. 619)

Notas de autor provistas por Syndetics

O.C. Zienkiewicz is Professor Emeritus at the Civil and Computational Engineering Centre, University of Wales Swansea, UK and the UNESCO Chair of Numerical Methods in Engineering at the Technical University of Catalunya, Spain
R.L. Taylor is a Professor in the Graduate School, Department of Civil Engineering and Environmental Engineering at the University of California, Berkeley, USA