Engineering analysis in imprecise geometric models

Holes, gaps, dangling boundaries and other imperfections of the geometric models preclude direct application of traditional engineering analysis tools. In such cases geometric inaccuracies have to be removed using a geometry “healing” (repair) procedure which results in a valid solid model. Repair procedure applied to the geometric model is computationally expensive and often requires human intervention and supervision. On the other hand, the repair procedure applied to the surface meshes derived from the boundaries of a geometric model may negatively affect the quality of the Finite Element mesh whose construction follows the repair procedure. s paper we describe a novel numerical technique that enables engineering analysis in imprecise geometric models without reconstructing a valid solid model. At the heart of the proposed method lies a modified geometrically adaptive integration technique. It uses a hybrid geometric model, that consists of a hierarchical space decomposition, boundary representation (B-rep) and distance fields. Hierarchical space decomposition helps to resolve the geometric imperfections, while the original geometric model is used to allocate the integration points in the boundary (geometry) cells. The proposed method uses solution structures that combine together the distance fields to the geometric boundaries, boundary conditions and basis functions to enforce the prescribed boundary conditions. proach has been verified on several numerical examples. Our numerical experiments confirm high reliability of the proposed engineering analysis approach for a wide range of geometric imperfections. Despite that the paper presents 2D examples the proposed approach can be generalized in 3D.