A Framework of the Meshless Method for Topology Optimization Using the Smooth-Edged Material Distribution for Optimizing Topology Method

Density variables based on nodal or Gaussian points are naturally incorporated in meshless topology optimization approaches, pursuing distinct topological layouts with solid and void solutions. However, engineering applications have been hampered by the fact that the authentic structure boundary cannot be identified without manual intervention. To alleviate this issue, the Smooth-Edged Material Distribution for Optimizing Topology (SEMDOT) method is developed within the context of meshless approximation. In meshless analysis, the non-overlap cell variables instead of nodal or Gaussian-based variables are adopted to characterize the existence or absence of sub-regions. This work proposes a non-penalized SEMDOT where an interpolation-based heuristic sensitivity expression is utilized. The 2D and 3D compliance minimization problems serve to validate the efficiency and applicability of the proposed non-penalized SEMDOT approach based on the framework of the meshless method. The numerical results demonstrated that the proposed approach is capable of generating final designs with continuous and smooth edges or surfaces.