Numerical investigations in non-watertight models based on a surface-independent discretization boundary element method

Abstract

It is well known that boundary integral equations are exact mathematical representations of the governing differential equations of a boundary value problem when the integrals are written over a closed-shape boundary representation (B-representation) of the domain, usually reffered to as a watertight B-representation. However, practical geometric design technics (namely, NURBS surfaces) often do not render a watertight B-representation. Non-watertight geometric models with small gaps and overlaps are often generated in the design stage of projects. Based on a proposed surface-independent discretization approach, the present study investigates how unsought gaps affect the response of boundary element models of linear elasticity problems. The developed surface-independent discretization is applied to discretize multiple-patches NURBS B-representation geometries. Linear triangular and quadrilateral elements are adopted to discretize the independent surfaces. Generalized discontinuous elements at the edges of the visible areas of the NURBS parametric spaces are detected by a Level Set function. An offset collocation strategy is adopted for the nodes at the edges of the visible part of the parametric spaces. Thus, singularities and near singularities due to collocation are avoided in the BEM equations. The influence of gaps in the convergence of the L2-norm of boundary displacement error is verified in a 3D example with an available analytical solution. A second example with available numerical solution is analyzed with a non-watertight BEM discretization for qualitative boundary field validation. Finally, a non-watertight B-representation geometry of a crane hook is analyzed. The obtained results have pointed out that, as long as the gaps (and overlaps) are small enough, BEM models built up from non-watertight geometries may produce valuable solutions for practical purposes.