Evaluation of Topology Optimization Filtering with Numeric Examples

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Commonly used filtering algorithms and settings for addressing the checkerboarding problem inherent in the continuous density-based topology optimization approach (e.g., the Solid Isotropic Material with Penalization or SIMP method) are discussed. A modification to the optimality criteria recursion relationship is shown, and an alternative formulation of optimality criteria (OC) suitable for use with a linear density filter is provided. A MATLAB implementation of a 2D compliance minimization problem using OC and the Globally Convergent Method of Moving Asymptotes (GCMMA) is used to compare the effects of using different filter weights, using a sensitivity or a linear density filter, and increasing the size of the filter. The 2D compliance problem is solved using commercially available topology optimization software including ANSYS workbench, TOSCA Structure, MSC Nastran, and Simcenter Nastran; comparisons are made to the MATLAB implementations of the problem to make inferences about the filter algorithms used in the commercial software. A 3D compliance problem is solved using Simcenter Nastran 2019.2 and TOSCA Structure 2019, and recommendations regarding element formulation and filter settings are provided.



Topology Optimization, Structural Optimization, GCMMA, Optimality Criteria, TOSCA, Nastran