Topology Optimization Based On B-spline And Finite Cell Method

In this paper,we proposed a NURBS-based finite cell method for topological optimization of structures with arbitrary shaped trimming design domain.NURBS basis is a standard for the geometric description in various CAD software,but there is no direct connection between CAD and CAE systems in terms of geometric descriptions.Enormous efforts are needed to transfer from CAD models to CAE models.It was reported that the pre-processing part of finite element analysis accounts for 80% of the whole finite element analysis time,which will undoubtedly reduce the efficiency of topology optimization.The combination of geometric analysis and finite cell method allows direct topological optimization of trimmed geometry derived from CAD system,which not only avoids data conversion,but also avoids time-consuming pre-processing such as mesh generation.Independent of the analysis domain,we introduce a high-order continuous NURBS to represent the density domain.It not only provides a built-in filter,but also achieves multi-resolution topology optimization,so that we can further refine the existing topology optimized structure.For the continuous density domain represented by NURBS,it is difficult to constrain the density domain geometrically because of the local support properties of NURBS.In this paper,we propose a simple and direct method to enforce geometric constraints of arbitrary shape in the process of topology optimization.Several numerical examples such as beams and slabs and practical engineering models are used to prove the effectiveness and accuracy of the proposed method.For the complicated structures such as plates and curved beams with holes,our method has unique advantages.