The Finite Element Method: Its Basis and FundamentalsElsevier, 26 mai 2005 - 752 pages The Sixth Edition of this influential best-selling book delivers the most up-to-date and comprehensive text and reference yet on the basis of the finite element method (FEM) for all engineers and mathematicians. Since the appearance of the first edition 38 years ago, The Finite Element Method provides arguably the most authoritative introductory text to the method, covering the latest developments and approaches in this dynamic subject, and is amply supplemented by exercises, worked solutions and computer algorithms. • The classic FEM text, written by the subject's leading authors • Enhancements include more worked examples and exercises • With a new chapter on automatic mesh generation and added materials on shape function development and the use of higher order elements in solving elasticity and field problems Active research has shaped The Finite Element Method into the pre-eminent tool for the modelling of physical systems. It maintains the comprehensive style of earlier editions, while presenting the systematic development for the solution of problems modelled by linear differential equations. Together with the second and third self-contained volumes (0750663219 and 0750663227), The Finite Element Method Set (0750664312) provides a formidable resource covering the theory and the application of FEM, including the basis of the method, its application to advanced solid and structural mechanics and to computational fluid dynamics.
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Table des matières
| 1 | |
| 19 | |
| 54 | |
| 103 | |
| 138 | |
Chapter 6 Problems in linear elasticity | 187 |
Chapter 7 Field problems heat conduction electric and magnetic potential and fluid flow | 229 |
Chapter 8 Automatic mesh generation | 264 |
Chapter 17 The time dimension discrete approximation in time | 589 |
Chapter 18 Coupled systems | 631 |
Chapter 19 Computer procedures for finite element analysis | 664 |
Matrix algebra | 668 |
Tensorindicial notation in the approximation of elasticity problems | 674 |
Solution of simultaneous linear algebraic equations | 683 |
Some integration formulae for a triangle | 692 |
Some integration formulae for a tetrahedron | 693 |
Chapter 9 The patch test reduced integration and nonconforming elements | 329 |
Chapter 10 Mixed formulation and constraints complete field methods | 356 |
Chapter 11 Incompressible problems mixed methods and other procedures of solution | 383 |
Chapter 12 Multidomain mixed approximations domain decomposition and frame methods | 429 |
Chapter 13 Errors recovery processes and error estimates | 456 |
Chapter 14 Adaptive finite element refinement | 500 |
Chapter 15 Pointbased and partition of unity approximations Extended finite element methods | 525 |
Chapter 16 The time dimension semidiscretization of field and dynamic problems and analytical solution procedures | 563 |
Some vector algebra | 694 |
Integration by parts in two or three dimensions Greens theorem | 699 |
Solutions exact at nodes | 701 |
Matrix diagonalization or lumping | 704 |
Author index | 711 |
Subject index | 719 |
Color Plate Section | 735 |
Expressions et termes fréquents
accuracy algorithm application approximation assumed Babuška behaviour boundary conditions Chapter coefficients Comp components computed consider constant convergence coordinates cubic curve defined Delaunay triangulation derivatives diagonal differential equations dimensions discontinuous discrete discussed displacement domain dynamic edge eigenvalues energy error estimator exact solution example finite element analysis finite element method finite element solution fluid formulation Galerkin given heat conduction hierarchical higher order incompressible interpolation isoparametric Lagrange multiplier lagrangian linear elastic load Mech moving least squares nodes Numer Meth O.C. Zienkiewicz obtained parameters patch test plane strain plane stress points polynomial pressure procedure quadratic quadrature quadrilateral elements R.L. Taylor rectangular residual satisfied shape functions shown in Fig simple singularity solved specified stability standard structure subdomains superconvergent surface mesh tetrahedral three-dimensional traction transformation triangle triangular element two-dimensional un+1 values variables variational principle vector weak form weighting function zero
Fréquemment cités
Page 670 - B are said to be conformable in the order AB if and only if the number of columns in A is equal to the number of rows in B.
Page 19 - OC ZIENK.IEWICZ and YK CHEUNG, 'The finite element method for analysis of elastic isotropic and orthotropic slabs', Proc.
Page 562 - Belytschko, T.: Non-planar 3D crack growth by the extended finite element and level sets - part ii: Level set update.
Page 20 - The displacement functions now define uniquely the state of strain within an element in terms of the nodal displacements. These strains, together with any initial strains and the...
Page 427 - Comp. Meth. Appl. Mech. Eng., 51, 3-29, 1985. 17.DS Malkus and TJR Hughes. Mixed finite element methods in reduced and selective integration techniques: a unification of concepts.
Page 500 - Y. Maday, AT Patera and J. Peraire. A general formulation for a posteriori bounds for output functionals of partial differential equations; application to the eigenvalue problem, C. R.
Page 428 - A general algorithm for compressible and incompressible flow. Part I: The split, characteristic based scheme', Int. j.
Page 561 - JM MELENK AND I. BABUSKA, The partition of unity finite element method: Basic theory and applications, Computer Methods in Applied Mechanics and Engineering, 39 (1996), pp.
Page 561 - Arbitrary branched and intersecting cracks with the extended finite element method. Int. J. Numer.
Page 325 - Construction of curvilinear co-ordinate systems and application to mesh generation'.