zbMATH — the first resource for mathematics

Plate stability by boundary element method. (English) Zbl 0768.73002
Lecture Notes in Engineering. 64. Berlin: Springer-Verlag. vii, 205 p. (1991).
The ambitious aim of this interesting book is to assess the validity, efficiency and versatility of the boundary element method (BEM) in elastic plate stability problems. For this the author gives at first (Chapter 2) a general account of the classical plate stability theory; an interesting feature of this presentation is the careful study of the formulation of the boundary conditions. In Chapter 3 are derived a boundary integral formulation and a boundary element solution of the linear equation of the membrane stress distribution for a plane stress problem. In Chapter 4 is presented a direct boundary element solution of the equation giving the critical buckling load. The accuracy of the method is tested by comparison with the results of the existing literature. In Chapter 5 a dual formulation is applied to the previous problem with the aim to transform domain integrals into boundary ones. The examples of numerical implementation presented by the author have many advantages over the same treated using domain discretization. The extension of the results of Chapter 3 and 4 to large deflections is presented in Chapter 6. An incremental approach is used with the deflection as the only domain unknown requiring modeling.
In all the methods discussed in the book “the modeling of the domain deflection appears to be a key factor in the accuracy and numerical efficiency of the solutions”, as points out the author in the Chapter 7. This is indeed one of the real challenges still facing the BEM applied to plate problems, the others being mainly the numerical treatment of singular and near-singular integrals.

74-02 Research exposition (monographs, survey articles) pertaining to mechanics of deformable solids
74S15 Boundary element methods applied to problems in solid mechanics
74K20 Plates
74G60 Bifurcation and buckling