T-Splines Based Isogeometric Topology Optimization with Arbitrarily Shaped Design Domains

摘要

In this paper, a new isogeometric topology optimization (ITO) method is proposed by using T-splines based isogeometric analysis (IGA). The arbitrarily shaped design domains, directly obtained from CAD, are represented by a single T-spline surface which overcomes the topological limitations of Non-Uniform Rational B-Spline (NURBS). The coefficients correlated with control points are directly used as design variables. Therefore, the T-spline basis functions applied for geometry description and calculation of structural response are simultaneously introduced to represent the density distribution. Several numerical examples show that the proposed approach leads to a coherent workflow to handle design problems of complicated structures. The optimized results are free of checkerboard patterns without additional stabilization and filtering techniques due to the properties of T-splines, which also simplified the post-processing. In addition, through performing local refinement, we can easily achieve multiresolution optimization and infill optimization within the T-splines based framework. In general, the proposed method provides a possibility to design, analyze, and optimize engineering structures in a uniform model, which has the potential to improve design efficiency and reduce the cost of product development.