This paper presents the development of a complete CAD-compatible framework for structural shape optimization in 3D. The boundaries of the domain are described using NURBS while the interior is discretized with B\'ezier tetrahedra. The tetrahedral mesh is obtained from the mesh generator software Gmsh. A methodology to reconstruct the NURBS surfaces from the triangular faces of the boundary mesh is presented. The description of the boundary is used for the computation of the analytical sensitivities with respect to the control points employed in surface design. Further, the mesh is updated at each iteration of the structural optimization process by a pseudo-elastic moving mesh method. In this procedure, the existing mesh is deformed to match the updated surface and therefore reduces the need for remeshing. Numerical examples are presented to test the performance of the proposed method. The use of the movable mesh technique results in a considerable decrease in the computational effort for the numerical examples.

翻译：本文提出了一个完整的CAD兼容三维结构形状优化框架。该框架使用NURBS描述域边界，利用贝塞尔四面体对内部进行离散化。四面体网格由网格生成软件Gmsh生成。本文提出了一种从边界网格三角形面重构NURBS曲面的方法，并利用边界描述计算相对于曲面设计中控制点的解析灵敏度。此外，在结构优化过程的每次迭代中，通过伪弹性移动网格方法更新网格。在此过程中，现有网格发生变形以匹配更新后的曲面，从而减少了重新网格化的需求。数值算例验证了所提方法的性能，结果表明可移动网格技术的使用显著降低了数值算例的计算成本。