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Record Nr. |
UNINA9911006699703321 |
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Autore |
Zienkiewicz O. C |
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Titolo |
Finite Elements and Approximation |
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Pubbl/distr/stampa |
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Newburyport, : Dover Publications, 2013 |
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ISBN |
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9781523125074 |
1523125071 |
9780486318011 |
048631801X |
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Edizione |
[1st ed.] |
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Descrizione fisica |
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1 online resource (574 p.) |
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Collana |
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Dover Books on Engineering |
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Altri autori (Persone) |
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Disciplina |
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Soggetti |
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Approximation theory |
Finite element method |
Engineering & Applied Sciences |
Applied Mathematics |
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Lingua di pubblicazione |
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Formato |
Materiale a stampa |
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Livello bibliografico |
Monografia |
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Note generali |
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Description based upon print version of record. |
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Nota di contenuto |
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Cover; Title Page; Copyright Page; Table of Contents; 1. Continuum Boundary Value Problems and The Need for Numerical Discretization. Finite Difference Methods; 1.1. Introduction,; 1.2. Some Examples of Continuum Problems,; 1.3. Finite Differences in One Dimension,; 1.4. Derivative Boundary Conditions,; 1.5. Nonlinear Problems,; 1.6. Finite Differences in More Than One Dimension,; 1.7. Problems Involving Irregularly Shaped Regions,; 1.8. Nonlinear Problems in More Than One Dimension,; 1.9. Approximation and Convergence,; 1.10. Concluding Remarks,; References,; Suggested Further Reading, |
2. Weighted Residual Methods: Use of Continuous Trial Functions2.1. Introduction-Approximation by Trial Functions,; 2.2. Weighted Residual Approximations,; 2.3. Approximation to the Solutions of Differential Equations and the Use of Trial Function-Weighted Residual Forms. Boundary Conditions Satisfied by Choice of Trial Functions,; 2.4. Simultaneous Approximation to the Solutions of Differential Equations and to the Boundary Conditions,; 2.5. Natural Boundary Conditions,; 2.6. Boundary Solution Methods,; 2.7. Systems of Differential Equations,; 2.8. Nonlinear Problems, |
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2.9. Concluding Remarks,References,; Suggested Further Reading,; 3. Piecewise Defined Trial Functions and The Finite Element Method; 3.1. Introduction-The Finite Element Concept,; 3.2. Some Typical Locally Defined Narrow-Base Shape Functions,; 3.3. Approximation to Solutions of Differential Equations and Continuity Requirements,; 3.4. Weak Formulation and the Galerkin Method,; 3.5. Some One-Dimensional Problems,; 3.6. Standard Discrete System. A Physical Analogue of the Equation Assembly Process,; 3.7. Generalization of the Finite Element Concepts for Two- and Three-Dimensional Problems, |
3.8. The Finite Element Method for Two-Dimensional Heat Conduction Problems,3.9. Two-Dimensional Elastic Stress Analysis Using Triangular Elements,; 3.10. Are Finite Differences a Special Case of the Finite Element Method?,; 3.11. Concluding Remarks,; References,; Suggested Further Reading,; 4. Higher Order Finite Element Approximation; 4.1. Introduction,; 4.2. Degree of Polynomial in Trial Functions and Convergence Rates,; 4.3. The Patch Test,; 4.4. Standard Higher Order Shape Functions for One-Dimensional Elements with C0 Continuity, |
4.5. Hierarchical Forms of Higher Order One-Dimensional Elements with C0 Continuity,4.6. Two-Dimensional Rectangular Finite Element Shape Functions of Higher Order,; 4.7. Two-Dimensional Shape Functions for Triangles,; 4.8. Three-Dimensional Shape Functions,; 4.9. Concluding Remarks,; References,; Suggested Further Reading,; 5. Mapping and Numerical Integration; 5.1. The Concept of Mapping,; 5.2. Numerical Integration,; 5.3. More on Mapping,; 5.4. Mesh Generation and Concluding Remarks,; References,; Suggested Further Reading,; 6. Variational Methods; 6.1. Introduction, |
6.2. Variational Principles, |
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Sommario/riassunto |
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A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o |
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