Unified Way for Dealing with Three-Dimensional Problems of Solid Elasticity

Abstract

Unified way for dealing with the problems of three dimensional solid, each type of plates and shells etc. was presented with the virtual boundary element least squares method(VBEM). It proceeded from the differential equations of three-dimensional theory of elasticity and employs the Kelvin solution and the least squares method. It is advantageous to the establishment of the models of a software for general application to calculate each type of three-dimensional problems of elasticity. Owing to directly employing the Kelvin solution and not citing any hypothesis, the numerical results of the method should be better than any others. The merits of the method are highlighted in comparison with the direct formulation of boundary element method (BEM). It is shown that coefficient matrix is symmetric and the treatment of singular integration is rendered unnecessary in the presented method. The examples prove the efficiency and calculating precision of the method.