Topology optimization for truss-like material distribution field with B-spline expression

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.