Boundary element analysis of 2D thin walled structures with high-order geometry elements using transformation

Thin structures have been widely designed and utilized in many industries. However, the analysis of the mechanical behavior of such structures represents a very challenging and attractive task to scientists and engineers because of their special geometrical shapes. The major difficulty in applying the boundary element method (BEM) to thin structures is the coinstantaneous existence of the singular and nearly singular integrals in conventional boundary integral equation (BIE). In this paper, a non-linear transformation over curved surface elements is introduced and applied to the indirect regularized boundary element method for 2-D thin structural problems. The developed transformation can remove or damp out the nearly singular properties of the integral kernels, based on the idea of diminishing the difference of the orders of magnitude or the scale of change of operational factors. For the test problems studied, 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.