did-you-know? rent-now

Amazon no longer offers textbook rentals. We do!

did-you-know? rent-now

Amazon no longer offers textbook rentals. We do!

We're the #1 textbook rental company. Let us show you why.

9780750663205

The Finite Element Method: Its Basis and Fundamentals

by ; ;
  • ISBN13:

    9780750663205

  • ISBN10:

    0750663200

  • Edition: 6th
  • Format: Hardcover
  • Copyright: 2005-04-18
  • Publisher: Elsevier Science
  • Purchase Benefits
  • Free Shipping Icon Free Shipping On Orders Over $35!
    Your order must be $35 or more to qualify for free economy shipping. Bulk sales, PO's, Marketplace items, eBooks and apparel do not qualify for this offer.
  • eCampus.com Logo Get Rewarded for Ordering Your Textbooks! Enroll Now
  • Write a Review Icon Write a Review
List Price: $137.00
  • Digital
    $151.88
    Add to Cart

    DURATION
    PRICE

Supplemental Materials

What is included with this book?

Summary

The sixth edition of these seminal books delivers the most up to date and comprehensive reference yet on the finite element method for all engineers and mathematicians. Renowned for their scope, range and authority, the new editions have been significantly developed in terms of both contents and scope. Each book is now complete in its own right and provides self-contained reference; used together they provide a formidable resource covering the theory and the application of the universally used FEM. Features New to This Edition- End of chapter exercises and worked examples- Instructor's Manual with worked solutions available online - Downloadable computer code In the years since the fifth edition was published, active research has continued to develop the Finite Element Method as the pre-eminent tool for the modelling of physical systems. Written by the leading professors in their fields, these new edition of the Finite Element Method maintains the comprehensive style of the earlier editions incorporate the latest developments in this dynamic subject. The three books cover the basis of the method, its application to solid mechanics and to fluid dynamics. * The classic introduction to the finite element method, by two of the subject's leading authors* Any professional or student of engineering involved in understanding the computational modelling of physical systems will inevitably use the techniques in this key text* Enhancements include more worked examples, exercises, plus a companion website with a worked solutions manual for tutors and downloadable algorithms

Table of Contents

Preface xiii
1 The standard discrete system and origins of the finite element method
1(18)
1.1 Introduction
1(2)
1.2 The structural element and the structural system
3(2)
1.3 Assembly and analysis of a structure
5(1)
1.4 The boundary conditions
6(1)
1.5 Electrical and fluid networks
7(2)
1.6 The general pattern
9(1)
1.7 The standard discrete system
10(1)
1.8 Transformation of coordinates
11(2)
1.9 Problems
13(6)
2 A direct physical approach to problems in elasticity: plane stress
19(35)
2.1 Introduction
19(1)
2.2 Direct formulation of finite element characteristics
20(11)
2.3 Generalization to the whole region - internal nodal force concept abandoned
31(3)
2.4 Displacement approach as a minimization of total potential energy
34(3)
2.5 Convergence criteria
37(1)
2.6 Discretization error and convergence rate
38(1)
2.7 Displacement functions with discontinuity between elements - non-conforming elements and the patch test
39(1)
2.8 Finite element solution process
40(1)
2.9 Numerical examples
40(6)
2.10 Concluding remarks
46(1)
2.11 Problems
47(7)
3 Generalization of the finite element concepts. Galerkin-weighted residual and variational approaches
54(49)
3.1 Introduction
54(3)
3.2 Integral or 'weak' statements equivalent to the differential equations
57(3)
3.3 Approximation to integral formulations: the weighted residual- Galerkin method
60(9)
3.4 Virtual work as the 'weak form' of equilibrium equations for analysis of solids or fluids
69(2)
3.5 Partial discretization
71(3)
3.6 Convergence
74(2)
3.7 What are 'variational principles'?
76(2)
3.8 'Natural' variational principles and their relation to governing differential equations
78(3)
3.9 Establishment of natural variational principles for linear, self-adjoint, differential equations
81(2)
3.10 Maximum, minimum, or a saddle point?
83(1)
3.11 Constrained variational principles. Lagrange multipliers
84(4)
3.12 Constrained variational principles. Penalty function and perturbed lagrangian methods
88(4)
3.13 Least squares approximations
92(3)
3.14 Concluding remarks - finite difference and boundary methods
95(2)
3.15 Problems
97(6)
4 'Standard' and 'hierarchical' element shape functions: some general families of C0 continuity
103(35)
4.1 Introduction
103(1)
4.2 Standard and hierarchical concepts
104(3)
4.3 Rectangular elements - some preliminary considerations
107(2)
4.4 Completeness of polynomials
109(1)
4.5 Rectangular elements - Lagrange family
110(2)
4.6 Rectangular elements - 'serendipity' family
112(4)
4.7 Triangular element family
116(3)
4.8 Line elements
119(1)
4.9 Rectangular prisms - Lagrange family
120(1)
4.10 Rectangular prisms - 'serendipity' family
121(1)
4.11 Tetrahedral elements
122(3)
4.12 Other simple three-dimensional elements
125(1)
4.13 Hierarchic polynomials in one dimension
125(3)
4.14 Two- and three-dimensional, hierarchical elements of the 'rectangle' or 'brick' type
128(1)
4.15 Triangle and tetrahedron family
128(2)
4.16 Improvement of conditioning with hierarchical forms
130(1)
4.17 Global and local finite element approximation
131(1)
4.18 Elimination of internal parameters before assembly - substructures
132(2)
4.19 Concluding remarks
134(1)
4.20 Problems
134(4)
5 Mapped elements and numerical integration - infinite' and 'singularity elements'
138(49)
5.1 Introduction
138(1)
5.2 Use of 'shape functions' in the establishment of coordinate transformations
139(4)
5.3 Geometrical conformity of elements
143(1)
5.4 Variation of the unknown function within distorted, curvilinear elements. Continuity requirements
143(2)
5.5 Evaluation of element matrices. Transformation in ξ η ζ coordinates
145(3)
5.6 Evaluation of element matrices. Transformation in area and volume coordinates
148(3)
5.7 Order of convergence for mapped elements
151(2)
5.8 Shape functions by degeneration
153(7)
5.9 Numerical integration - one dimensional
160(2)
5.10 Numerical integration - rectangular (2D) or brick regions (3D)
162(2)
5.11 Numerical integration - triangular or tetrahedral regions
164(1)
5.12 Required order of numerical integration
164(5)
5.13 Generation of finite element meshes by mapping. Blending functions
169(1)
5.14 Infinite domains and infinite elements
170(6)
5.15 Singular elements by mapping - use in fracture mechanics, etc.
176(1)
5.16 Computational advantage of numerically integrated finite elements
177(1)
5.17 Problems
178(9)
6 Problems in linear elasticity
187(42)
6.1 Introduction
187(1)
6.2 Governing equations
188(13)
6.3 Finite element approximation
201(6)
6.4 Reporting of results: displacements, strains and stresses
207(2)
6.5 Numerical examples
209(8)
6.6 Problems
217(12)
7 Field problems - heat conduction, electric and magnetic potential and fluid flow
229(35)
7.1 Introduction
229(1)
7.2 General quasi-harmonic equation
230(3)
7.3 Finite element solution process
233(4)
7.4 Partial discretization - transient problems
237(2)
7.5 Numerical examples - an assessment of accuracy
239(14)
7.6 Concluding remarks
253(1)
7.7 Problems
253(11)
8 Automatic mesh generation
264(65)
8.1 Introduction
264(2)
8.2 Two-dimensional mesh generation - advancing front method
266(20)
8.3 Surface mesh generation
286(17)
8.4 Three-dimensional mesh generation - Delaunay triangulation
303(20)
8.5 Concluding remarks
323(1)
8.6 Problems
323(6)
9 The patch test, reduced integration, and non-conforming elements
329(27)
9.1 Introduction
329(1)
9.2 Convergence requirements
330(2)
9.3 The simple patch test (tests A and B) - a necessary condition for convergence
332(2)
9.4 Generalized patch test (test C) and the single-element test
334(2)
9.5 The generality of a numerical patch test
336(1)
9.6 Higher order patch tests
336(1)
9.7 Application of the patch test to plane elasticity elements with 'standard' and 'reduced' quadrature
337(6)
9.8 Application of the patch test to an incompatible element
343(4)
9.9 Higher order patch test - assessment of robustness
347(1)
9.10 Concluding remarks
347(3)
9.11 Problems
350(6)
10 Mixed formulation and constraints - complete field methods 356(27)
10.1 Introduction
356(2)
10.2 Discretization of mixed forms - some general remarks
358(2)
10.3 Stability of mixed approximation. The patch test
360(3)
10.4 Two-field mixed formulation in elasticity
363(7)
10.5 Three-field mixed formulations in elasticity
370(5)
10.6 Complementary forms with direct constraint
375(4)
10.7 Concluding remarks - mixed formulation or a test of element 'robustness'
379(1)
10.8 Problems
379(4)
11 Incompressible problems, mixed methods and other procedures of solution 383(46)
11.1 Introduction
383(1)
11.2 Deviatoric stress and strain, pressure and volume change
383(1)
11.3 Two-field incompressible elasticity (u-ρ form)
384(9)
11.4 Three-field nearly incompressible elasticity (u-ρ-epsilonv form)
393(5)
11.5 Reduced and selective integration and its equivalence to penalized mixed problems
398(6)
11.6 A simple iterative solution process for mixed problems: Uzawa method
404(3)
11.7 Stabilized methods for some mixed elements failing the incompressibility patch test
407(14)
11.8 Concluding remarks
421(1)
11.9 Problems
422(7)
12 Multidomain mixed approximations - domain decomposition and 'frame' methods 429(27)
12.1 Introduction
429(1)
12.2 Linking of two or more subdomains by Lagrange multipliers
430(6)
12.3 Linking of two or more subdomains by perturbed lagrangian and penalty methods
436(6)
12.4 Interface displacement 'frame'
442(3)
12.5 Linking of boundary (or Trefftz)-type solution by the 'frame' of specified displacements
445(6)
12.6 Subdomains with 'standard' elements and global functions
451(1)
12.7 Concluding remarks
451(1)
12.8 Problems
451(5)
13 Errors, recovery processes and error estimates 456(44)
13.1 Definition of errors
456(3)
13.2 Superconvergence and optimal sampling points
459(6)
13.3 Recovery of gradients and stresses
465(2)
13.4 Superconvergent patch recovery - SPR
467(7)
13.5 Recovery by equilibration of patches - REP
474(2)
13.6 Error estimates by recovery
476(2)
13.7 Residual-based methods
478(10)
13.8 Asymptotic behaviour and robustness of error estimators - the Babuška patch test
488(2)
13.9 Bounds on quantities of interest
490(4)
13.10 Which errors should concern us?
494(1)
13.11 Problems
495(5)
14 Adaptive finite element refinement 500(25)
14.1 Introduction
500(3)
14.2 Adaptive h-refinement
503(11)
14.3 ρ-refinement and hρ-refinement
514(4)
14.4 Concluding remarks
518(2)
14.5 Problems
520(5)
15 Point-based and partition of unity approximations. Extended finite element methods 525(38)
15.1 Introduction
525(2)
15.2 Function approximation
527(6)
15.3 Moving least squares approximations - restoration of continuity of approximation
533(5)
15.4 Hierarchical enhancement of moving least squares expansions
538(2)
15.5 Point collocation - finite point methods
540(6)
15.6 Galerkin weighting and finite volume methods
546(3)
15.7 Use of hierarchic and special functions based on standard finite elements satisfying the partition of unity requirement
549(9)
15.8 Concluding remarks
558(1)
15.9 Problems
558(5)
16 The time dimension - semi-discretization of field and dynamic problems and analytical solution procedures 563(26)
16.1 Introduction
563(1)
16.2 Direct formulation of time-dependent problems with spatial finite element subdivision
563(7)
16.3 General classification
570(1)
16.4 Free response - eigenvalues for second-order problems and dynamic vibration
571(5)
16.5 Free response - eigenvalues for first-order problems and heat conduction, etc.
576(2)
16.6 Free response - damped dynamic eigenvalues
578(1)
16.7 Forced periodic response
579(1)
16.8 Transient response by analytical procedures
579(4)
16.9 Symmetry and repeatability
583(1)
16.10 Problems
584(5)
17 The time dimension - discrete approximation in time 589(42)
17.1 Introduction
589(1)
17.2 Simple time-step algorithms for the first-order equation
590(10)
17.3 General single-step algorithms for first- and second-order equations
600(9)
17.4 Stability of general algorithms
609(6)
17.5 Multistep recurrence algorithms
615(3)
17.6 Some remarks on general performance of numerical algorithms
618(1)
17.7 Time discontinuous Galerkin approximation
619(5)
17.8 Concluding remarks
624(2)
17.9 Problems
626(5)
18 Coupled systems 631(33)
18.1 Coupled problems - definition and classification
631(3)
18.2 Fluid-structure interaction (Class I problems)
634(11)
18.3 Soil-pore fluid interaction (Class II problems)
645(8)
18.4 Partitioned single-phase systems - implicit-explicit partitions (Class I problems)
653(2)
18.5 Staggered solution processes
655(5)
18.6 Concluding remarks
660(4)
19 Computer procedures for finite element analysis 664(4)
19.1 Introduction
664(1)
19.2 Pre-processing module: mesh creation
664(2)
19.3 Solution module
666(1)
19.4 Post-processor module
666(1)
19.5 User modules
667(1)
Appendix A: Matrix algebra 668(6)
Appendix B: Tensor-indicial notation in the approximation of elasticity problems 674(9)
Appendix C: Solution of simultaneous linear algebraic equations 683(9)
Appendix D: Some integration formulae for a triangle 692(1)
Appendix E: Some integration formulae for a tetrahedron 693(1)
Appendix F: Some vector algebra 694(5)
Appendix G: Integration by parts in two or three dimensions (Green's theorem) 699(2)
Appendix H: Solutions exact at nodes 701(3)
Appendix I: Matrix diagonalization or lumping 704(7)
Author index 711(8)
Subject index 719

Supplemental Materials

What is included with this book?

The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any access cards, study guides, lab manuals, CDs, etc.

The Used, Rental and eBook copies of this book are not guaranteed to include any supplemental materials. Typically, only the book itself is included. This is true even if the title states it includes any access cards, study guides, lab manuals, CDs, etc.

Rewards Program