The finite element method its basis and fundamentals
Title:
The finite element method its basis and fundamentals
Author:
Zienkiewicz, O. C.
ISBN:
9780080472775
Personal Author:
Edition:
6th ed.
Publication Information:
Amsterdam ; Boston : Elsevier Butterworth-Heinemann, 2005.
Physical Description:
1 online resource (xiv, 733 pages, [4] pages of plates) : illustrations (some color)
General Note:
"In the present edition we have decided not to pursue the course of having three contiguous volumes but rather we treat the whole work as an assembly of three separate works, each one capable of being used without the others ... The two further volumes form again separate books ... The first of these is entitled The Finite Element Method in Solid and Structural Mechanics and the second is a text entitled The Finite Element Method in Fluid Dynamics."--Preface.
Contents:
Cover -- Title page -- Copyright page -- Table of contents -- Preface -- 1. The standard discrete system and origins of the finite element method -- 1.1 Introduction -- 1.2 The structural element and the structural system -- 1.3 Assembly and analysis of a structure -- 1.4 The boundary conditions -- 1.5 Electrical and fluid networks -- 1.6 The general pattern -- 1.7 The standard discrete system -- 1.8 Transformation of coordinates -- 1.9 Problems -- 2. A direct physical approach to problems in elasticity: plane stress -- 2.1 Introduction -- 2.2 Direct formulation of finite element characteristics -- 2.3 Generalization to the whole region -- internal nodal force concept abandoned -- 2.4 Displacement approach as a minimization of total potential energy -- 2.5 Convergence criteria -- 2.6 Discretization error and convergence rate -- 2.7 Displacement functions with discontinuity between elements -- non-conforming elements and the patch test -- 2.8 Finite element solution process -- 2.9 Numerical examples -- 2.10 Concluding remarks -- 2.11 Problems -- 3. Generalization of the finite element concepts. Galerkin- weighted residual and variational approaches -- 3.1 Introduction -- 3.2 Integral or 'weak' statements equivalent to the differential equations -- 3.3 Approximation to integral formulations: the weighted residual-Galerkin method -- 3.4 Virtual work as the 'weak form' of equilibrium equations for analysis of solids or fluids -- 3.5 Partial discretization -- 3.6 Convergence -- 3.7 What are 'variational principles'? -- 3.8 'Natural' variational principles and their relation to governing differential equations -- 3.9 Establishment of natural variational principles for linear, self-adjoint, differential equations -- 3.10 Maximum, minimum, or a saddle point? -- 3.11 Constrained variational principles. Lagrange multipliers -- 3.12 Constrained variational principles. Penalty function and perturbed lagrangian methods -- 3.13 Least squares approximations -- 3.14 Concluding remarks -- finite difference and boundary methods -- 3.15 Problems -- 4. 'Standard' and 'hierarchical' element shape functions: some general families of C0 continuity -- 4.1 Introduction -- 4.2 Standard and hierarchical concepts -- Part 1. 'Standard' shape functions -- Two-dimensional elements -- One-dimensional elements -- Three-dimensional elements -- Part 2. Hierarchical shape functions -- 4.13 Hierarchic polynomials in one dimension -- 4.14 Two- and three-dimensional, hierarchical elements of the 'rectangle' or 'brick' type -- 4.15 Triangle and tetrahedron family -- 4.16 Improvement of conditioning with hierarchical forms -- 4.17 Global and local finite element approximation -- 4.18 Elimination of internal parameters before assembly -- substructures -- 4.19 Concluding remarks -- 4.20 Problems -- 5. Mapped elements and numerical integration -- 'infinite' and 'singularity elements' -- 5.1 Introduction -- 5.2 Use of 'shape functions' in the establishment of coordinate tran.
Abstract:
Annotation 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.<br /><br />. The classic FEM text, written by the subject's leading authors<br />. Enhancements include more worked examples and exercises, plus a companion website with a solutions manual and downloadable algorithms<br />. 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<br /><br />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.<br /><br />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.<br /><br />* The classic introduction to the finite element method, by two of the subject's leading authors<br />* Any professional or student of engineering involved in understanding the computational modelling of physical systems will inevitably use the techniques in this key text<br />* Enhancements include more worked examples, exercises, plus a companion website with a worked solutions manual for tutors and downloadable algorithms.
Genre:
Electronic Access:
Knovel http://app.knovel.com/web/toc.v/cid:kpFEMIBFEA