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.

在这项工作中，基于有限元方法（FCM），开发了一种自适应T样条有限元方法，用于结构形状优化。该方法的优点是在均匀B网格上使用局部T网格细化，以确保形状优化过程中的良好计算精度。为此，我们首先使用均匀的粗网格对结构进行预分析，而计算量却相对较低。然后，通过采用应力梯度准则来识别用于局部细化的单元。随后，采用基于自适应四叉树的细化方案来生成自适应T网格，该网格保留相应T样条曲线形状函数的线性独立性。最后，相应地建立形状优化框架，数值算例验证了所提出的自适应细化方案。机械结构的形状优化程序充分证明了其效率。