Finite Element Methods for Structures with Large Stochastic Variations by I. Elishakoff and Y.J. Ren, Oxford University Press, Oxford, 2003, pp. ix+260, price £45, ISBN 0 19 852631 8
✍ Scribed by C.W.S. To
- Publisher
- Elsevier Science
- Year
- 2004
- Tongue
- English
- Weight
- 152 KB
- Volume
- 270
- Category
- Article
- ISSN
- 0022-460X
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✦ Synopsis
This book contains 260pp. It has seven chapters, a prologue and an epilogue, 11 appendices and a bibliography with over a thousand references. An author and subject indices are also included. The style of the book is typical of that of the senior author in the sense that everywhere in the book shows that the authors read widely and the senior author collaborated his research work with many international workers. In the prologue it contains an interesting or arguably somewhat stretched but brief introduction to the history of the finite element method (FEM).
It is mentioned in the prologue that the authors prefer the term, finite element method for stochastic problems (FEMSP) instead of stochastic finite element method (SFEM). This reviewer thinks that while FEMSP is an improvement over SFEM it is too general since it can include temporally stochastic loadings or spatially stochastic problems or both. Therefore, a more appropriate term for the problems dealt with in the above book would be finite element method for spatially stochastic problems (FEMSSP).
Returning to the individual chapters of the book, Chapter 1 is concerned with the fundamentals of the FEM. The formulations included are for beam bending and plane stress/strain analyses. The formulations are of the displacement type and the treatments here are very elementary. Readers looking for more advanced topics will be disappointed.
Chapter 2 presents a brief review of the FEM for stochastic structures. The techniques included in this chapter are: finite element formulation (FEF) by the perturbation technique, FEF by series expansion, FEF by homogeneous chaos, improved first order perturbation FEF, and numerical results for a two-bar truss with stochastic Young's moduli. This chapter concludes with illustrations of various simple examples. Results and discussion of the examples are also presented.
Chapters 3-5 present several new approaches which are not perturbative FEM for stochastic structures. In Chapter 3, considerable length is devoted to the FEM based on the exact inverse of the stiffness matrices of a bar and beam by Fuch's method. It should be pointed out that for a linear uniform bar and beam their element stiffness matrices can be obtained explicitly, in the sense that no numerical matrix inversion and numerical integration are required. These explicit stiffness matrices can lead to exact displacement solutions. For example, the stiffness matrix of a uniform bar has been obtained explicitly by selecting linear polynomials for the shape functions. Similarly, the stiffness matrix of a uniform Bernoulli-Euler beam has been obtained explicitly by selecting cubic polynomial shape functions and exact solution can be obtained accordingly. In this chapter the so-called new formulation of the finite element stiffness matrix is presented. The