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Computational Methods in Solid Mechanics : Developments in Hydrobiology - Alain Curnier

Computational Methods in Solid Mechanics

Developments in Hydrobiology

Hardcover Published: 31st May 1994
ISBN: 9780792327615
Number Of Pages: 404

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Summary This bookis an introdU(;tion to the three numerical methodsmost commonly used for the mechanical analysisof deformable solids, namely: - the finite element method(FEM), a particularcaseofGalerkin's method, for the spatial discretisationofsolids; - the linear iteration method(LIM), a generalizationofNewton's method, for solving geometricandmaterial nonlinearities; - the finite difference method (FDM), in fact Newmark's method, for the temporal discretisation oftheproblem. The main reason for this selection is the degree of generality reached by the computerprograms basedon the combinationofthese methods. The originalityofthepresentation lies in the comparable emphasisputon the spatial, temporal and nonlinear dimensions of problem solving. For each dimension, there corresponds one method whose basic principle is exposed. It is then shown how they can be combined in a compact and flexible fonn. Thisjoint investigationofthe three methods leads to a particularly neat global algorithm. It is with this double objectiveof simplicity and unity in mind that this book has been designed. An outline of the book follows. A one-dimensional bar model problem, including all the ingredients necessary for acompletepresentationofthe addressed methods, isdefined in Chapter1. Emphasis is placedon the virtual work principle as an alternative to the.differentialequation ofmotion. Chapters 2, 3 and 4 present the three numerical methods: FEM, LIM and FDM, respectively. Although the presentation relies on a one-dimensional model problem, the fonnalism used is general and directly extendible to two- and three-dimensional situations. The compact combination of the three methods is discussed in detail in Chapter 5, which also contains several sections concerning their computer implementation.

Introductionp. 1
One-Dimensional Bar Model Problem (Principle of Virtual Work)p. 5
Spatial Discretisation by the Finite Element Methodp. 55
Solution of Non-Linearities by the Linear Iteration Methodp. 119
Time Integration by the Finite Difference Methodp. 183
Compact Combination of the Finite Element, Linear Iteration and Finite Difference Methodsp. 231
Two- and Three-Dimensional Deformable Solidsp. 267
Conclusionp. 349
Bibliographyp. 350
Appendix A: List of Symbolsp. 351
Appendix B: Exercisesp. 361
Indexp. 393
Table of Contents provided by Blackwell. All Rights Reserved.

ISBN: 9780792327615
ISBN-10: 0792327616
Series: Developments in Hydrobiology
Audience: General
Format: Hardcover
Language: English
Number Of Pages: 404
Published: 31st May 1994
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 23.39 x 15.6  x 2.39
Weight (kg): 0.76

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