Even through the topology optimal truss-like structure based on the truss-like material model is very close to its analytical solution, further post-processing is required to form a truss or a homogeneous isotropic perforated plate. In this paper, an optimal truss-like material distribution field is expressed by a B-spline function. For the convenience of processing, the optimal material distribution domain of a truss-like structures is firstly extended into a curved quadrilateral extension domain. Then, the relationship between the B-spline curve clusters and the distribution of truss-like material members is established by a sample points array. Combined with the distribution of materials, a topology structure that meets the design requirements is formed. Numerical examples with three models show that the B-spline function can describe the distribution field of truss-like material members efficiently, and the number of the truss-like material members can be actively controlled to meet different design needs. Comparison between the optimal results and them of the traditional analytical solution is made and results show that the topological structure is close to the analytical solution.

即使基于类桁架材料模型的拓扑优化类桁架结构与其解析解非常接近，但仍需要进一步的后处理以形成桁架或均质各向同性穿孔板。在本文中，最佳桁架状材料分布场由 B 样条函数表示。为便于加工，首先将类桁架结构的最佳材料分布域扩展为曲线四边形扩展域。然后，通过采样点阵列建立B样条曲线簇与类桁架材料构件分布之间的关系。结合材料的分布，形成符合设计要求的拓扑结构。三个模型的数值算例表明，B样条函数可以有效地描述类桁架材料构件的分布场，并且可以主动控制类桁架材料构件的数量以满足不同的设计需求。将优化结果与传统解析解的优化结果进行比较，结果表明拓扑结构与解析解很接近。