On the development and application of a modified boundary element method for the analysis of three-dimensional elastostatic problems in thick plates

Citation

Lu, Lingyun (1992) On the development and application of a modified boundary element method for the analysis of three-dimensional elastostatic problems in thick plates. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/tkxp-f839. https://resolver.caltech.edu/CaltechETD:etd-08072007-131209

Abstract

A modified three-dimensional Boundary Element Method (BEM) is developed. This method is specially tailored towards applications in three-dimensional elasticity, involving regions containing two parallel planar surfaces. Typical structures are the three-dimensional plate structures. The formulation makes use of the three-dimensional fundamental solution of a concentrated load applied in an infinite three-dimensional plate of uniform finite thickness (obtained by Benitez and Rosakis in 1985). The most attractive feature of this modified BEM is that, for the class of problems involving structures described above subjected to traction-free boundary conditions on the planar surfaces, discretization is only required on the lateral surfaces of the plate and the surfaces of the cavities, holes, and cracks in the plate. No discretization is needed on the planar surfaces of the plate. In this initial study, three problems involving a pressurized hole in an infinite three-dimensional plate are analyzed. The shapes of the holes include a circular hole and two elliptical holes with the aspect ratios of 4 and 10, respectively. In all the cases, the accuracy of the modified BEM is established by direct comparison of its results with those of finite element calculations. The results of the modified BEM are also compared with the plane-stress and plane-strain approximations of the problems under consideration. This comparison make it possible to access the important three-dimensional effects near the surface of the elliptical hole.

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