Isogeometric Shell Analysis of Multi-sided CAD Geometries Using Toric Surfaces

Abstract

To address the challenges associated with multi-sided shells in traditional isogeometric analysis (IGA), this paper introduces a novel isogeometric shell method for trimmed CAD geometries based on toric surfaces and Reissner–Mindlin shell theory. By utilizing toric surface patches, both trimmed and untrimmed elements of the CAD surfaces are represented through a unified geometric framework, ensuring continuity and an accurate geometric description. Toric-Bernstein basis functions are employed to accurately interpolate the geometry and displacement of the trimmed shell. For singularities and corner points on the toric surface, the normal vector is defined as the unit directional vector from the center of curvature to the corresponding control point. Several numerical examples of polygonal shells are presented to evaluate the effectiveness and robustness of the proposed method. This approach significantly simplifies the treatment of trimmed shell IGA and provides a promising solution for simulating complex shell structures with intricate boundaries.