Improved hole and tube elements in BEM for elasticity problems

Structures with holes are prevalent in engineering applications. Analyzing the stress concentration effects caused by holes using the finite element method (FEM) or the boundary element method (BEM) is challenging and timeconsuming. Typically, a large number of elements are necessary in the vicinity of holes to achieve accurate results. In this paper, a series of improved hole elements and tube elements are constructed for simulating the holes and cylinders, respectively. Two construction methods for hole elements, based on Lagrange and trigonometric interpolations, respectively, are introduced. The general formulas for evaluating singular integrals over the proposed elements are derived. Additionally, the adaptive element sub-division technique is applied to address the nearly singular integrals over these elements and account for the interactions of multiple holes. Five numerical examples are studied to demonstrate the accuracy and efficiency of the proposed elements. The results demonstrate that employing hole and tube elements can reduce the number of nodes while maintaining stress accuracy, in comparison to using several quadratic elements.