The Finite Element Method: Its Basis and Fundamentals
Butterworth-Heinemann, May 26, 2005 - Technology & Engineering - 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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some general families of C0 continuity
Chapter 5 Mapped elements and numerical integration infinite and singularity elements
Chapter 6 Problems in linear elasticity
Chapter 7 Field problems heat conduction electric and magnetic potential and fluid flow
Chapter 8 Automatic mesh generation
Chapter 17 The time dimension discrete approximation in time
Chapter 18 Coupled systems
Chapter 19 Computer procedures for finite element analysis
Tensorindicial notation in the approximation of elasticity problems
Solution of simultaneous linear algebraic equations
Some integration formulae for a triangle
Some integration formulae for a tetrahedron
Chapter 9 The patch test reduced integration and nonconforming elements
Chapter 10 Mixed formulation and constraints complete field methods
Chapter 11 Incompressible problems mixed methods and other procedures of solution
Chapter 12 Multidomain mixed approximations domain decomposition and frame methods
Chapter 13 Errors recovery processes and error estimates
Chapter 14 Adaptive finite element refinement
Chapter 15 Pointbased and partition of unity approximations Extended finite element methods
Chapter 16 The time dimension semidiscretization of field and dynamic problems and analytical solution procedures
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
Page 19 - OC ZIENK.IEWICZ and YK CHEUNG, 'The finite element method for analysis of elastic isotropic and orthotropic slabs', Proc.