Analysis of 3D linear elasticity problems directly on geometric model with the boundary face method

This paper presents the boundary face method (BFM) based on boundary integral equations for solving 3D linear elasticity problems directly on geometric model. In the method, both boundary integration and variable approximation are performed in the parametric space of each boundary face. The geometric data at Gaussian integration points, such as the coordinates, the Jacobians and the outward normal, are calculated directly from the faces rather than from elements, and thus no geometric error will be introduced. The BFM has real potential to completely integrate with CAD system, because its implementation can be directly based on a CAD model through its boundary representation data. The structures with local small features are directly used for analysis, when all of geometry features are kept accurately according to their size in the real-world-coordinate system, instead of simplification for them. Numerical examples demonstrate that the proposed method effectively simulates thin shell based on 3D elastic theory and the complicated structure with detailed configurations in a simple way, and also provides more accurate results when compared with the finite element method (FEM).