Three-dimensional stress analysis of thin structures using a boundary element method with sinh transformation for nearly singular integrals

Abstract

In this work a three dimensional (3D) boundary element method was established with an efficient nonlinear coordinate transformation scheme, namely sinh transformation, to evaluate nearly singular integrals in boundary integral formulations. Second-order quadrilateral surface elements were developed based on this method to accurately describe the geometry of thin structures. The elastic behaviors of selected thin structures were then computed by using the 3D boundary element model to demonstrate the accuracy and efficiency of this approach. A number of testing examples, i.e., the 3D Kirsch problem, the thin spherical shell problem, the ellipsoidal vessel problem with non-uniform thickness and the hollow circular cylinder problem, were numerically studied to test the established method. Remarkable accuracy and efficiency were found in the developed approach through the comparison to the numerical results and analytical solutions reported in the literature.