Topology Optimization with Tetra-kai-decahedra and Spheroidal Masks

TL;DR

This paper introduces a new 3D topology optimization method using a tetra-kai-decahedron mesh and spheroidal masks, improving connectivity and eliminating singularities in the solution space.

Contribution

It presents a novel meshing scheme based on truncated octahedron cells and extends the MMOS method to 3D with spheroidal negative masks, enhancing topology optimization techniques.

Findings

Improved face connectivity reduces singular solutions.

Effective 3D density computation and sensitivity analysis.

Successful application to structural optimization problems.

Abstract

A novel meshing scheme, based on regular tetra-kai-decahedron, also referred to as truncated octahedron, cells is presented for use in spatial topology optimization. A tetra-kai-decahedron mesh ensures face connectivity between elements thereby eliminating singular solutions from the solution space. Various other benefits of implementing the said mesh are also highlighted, and the corresponding finite element is introduced. Material mask overlay strategy or MMOS, a feature based method for topology optimization is extended for use in 3-dimensions (MMOS-3D) via the aforementioned finite element and spheroidal negative masks. Formulation for density computation and sensitivity analysis for gradient based optimization is developed. Examples on traditional structural topology optimization problems are presented with detailed discussion on efficacy of the proposed approach.