The finite element method : its basis and fundamentals /

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Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Zienkiewicz, O. C.
Otros Autores: Taylor, Robert L. (Robert Leroy), 1934-, Zhu, J. Z.
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Amsterdam ; Boston : Elsevier Butterworth-Heinemann, 2005.
Edición:6th ed.
Temas:
Finite element method.
Engineering mathematics.
Engineering mathematics > Data processing.
Méthode des éléments finis.
Mathématiques de l'ingénieur > Informatique.
Mathématiques de l'ingénieur.
TECHNOLOGY & ENGINEERING > Engineering (General)
TECHNOLOGY & ENGINEERING > Reference.
Engineering mathematics > Data processing
Engineering mathematics
Finite element method
dissertations.
Academic theses
Academic theses.
Thèses et écrits académiques.
Acceso en línea:Texto completo
Tabla de Contenidos:
  • 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.

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