Topology optimization guided by a geometrical pattern library

This work proposes an approach for structural Topology Optimization enforcing geometrical features on optimized designs using a predefined library of geometrical patterns. The approach applies a density-based Topology Optimization subject to a geometrical constraint guiding the design toward shapes matching the geometrical features found in the predefined pattern library.

Multiple distance measures and suitable matching algorithms are studied to calculate local mappings between the design in each optimization iteration and the pattern library. An aggregated appearance constraint is evaluating the pattern matching. The gradient of the appearance constraint, objective function, and other constraints are applied in a gradient-based optimization scheme.

A parameter for the appearance constraint dictates how closely the design should match the patterns defined in the library. The convergence behavior is studied on a variety of 2D and 3D optimization scenarios. The formulation is also applied to design variables controlling the material orientations alongside the material density as well as other optimization objectives such as stress minimization.