Meshless stress analysis of nonhomogeneous materials by triple-reciprocity boundary element method

Abstract

In general, internal cells are required to solve nonhomogeneous elastic problems using a conventional boundary element method (BEM). However, in this case, the merit of the BEM, which is an ease of data preparation, is lost. In this study, it is shown that two-dimensional nonhomogeneous elastic problems of functionally gradient materials can be solved without the use of internal cells, using the triple-reciprocity BEM. The triple-reciprocity BEM can be applied to thermo-elastoplastic problems with arbitrary heat generation and to three-dimensional elastoplastic problems without internal cells. In this paper, Young's modulus and Poisson's ratio are variable in nonhomogeneous elastic materials. In this method, boundary elements and arbitrary internal points are used. The distribution of fictitious body force generated by a nonhomogeneous material is interpolated using boundary integral equations. This interpolation corresponds to a thin plate spline. In this paper, elastic analysis is carried out for laminated materials, porous materials and a particle-dispersed composite as special cases of functionally gradient materials. In the case of composite materials or a layer structure, the distribution of Lame's constant is not continuous. However, the same interpolation method can be used for special case of nonhomogeneous material. A new computer program is developed and applied to several nonhomogeneous elastic problems to clearly demonstrate the theory.