Analysis of 2D Thin Walled Structures in BEM with High-Order Geometry Elements Using Exact Integration

Abstract

There exist nearly singular integrals for thin walled structures in the boundary element method (BEM). In this paper, an efficient analytical method is developed to deal with the nearly singular integrals in the boundary integral equations (BIEs) for 2-D thin walled structures. The developed method is possible for problems defined in high-order geometry elements when the nearly singular integrals need to be calculated. For the analysis of nearly singular integrals with high-order geometry elements, much fewer boundary elements can be used to achieve higher accuracy. More importantly, computational models of thin walled structures or thin shapes in structures demand a higher level of the geometry approximation to the original domains, and the usage of high-order geometry in computational models can meet this requirement. Three numerical examples are presented to test the developed method and very promising results are obtained when the thickness-to-length ratio is in the orders of 1E-01 to 1E-06, which is sufficient for modeling most thin structures in industrial applications.