An adaptive T-spline finite cell method for structural shape optimization

In this work, an adaptive T-spline finite cell method is developed for structural shape optimization based on the finite cell method (FCM). This method has the advantage of using local T-mesh refinement on the uniform B-mesh to ensure a good computing accuracy in the shape optimization process. To do this, we first carry out a pre-analysis of the structure using a uniform coarse mesh with relatively low computational effort. Then, cells for local refinements are identified by adopting the stress gradient criterion. Subsequently, an adaptive quadtree-based refinement scheme is employed to generate the adaptive T-mesh which preserves the linear independence of the corresponding T-spline shape functions. Finally, the shape optimization framework is correspondingly established, and the proposed adaptive refinement scheme is validated by numerical examples. Its efficiency is fully demonstrated by shape optimization procedures of mechanical structures.