Structural topology optimization method based on geometry shape parameters

This work presents a geometric feature-based structural topology optimization approach that directly obtains topological configurations using the boundaries of basic geometry. Here, we assume that the topological configuration is a combination of a set of basic geometries defined by the same Non-Uniform Rational B-spline (NURBS) parameters. Within the design domain, the geometric boundary distribution position field is delineated through the utilization of mesh node and geometry boundary normal vectors. The explicit geometry mapping function is constructed by integrating the field values of all the boundaries within the geometry, which allows for the calculation of the proportion of mesh occupied by the geometries using step function. The relative density of each mesh can then be calculated. This allows the equations to be iterated and complex design results to be obtained. In the optimization process, the design variables are the geometric parameters of each individual geometry. And the Method of Moving Asymptotes (MMA) method is selected to update these design variables. Numerical examples are shown to validate the correctness and superiority of this proposed method.