Overhang penalization in additive manufacturing via phase field structural topology optimization with anisotropic energies

TL;DR

This paper introduces a phase field method for structural topology optimization in additive manufacturing that effectively penalizes overhangs using anisotropic energies, supported by mathematical analysis and numerical results.

Contribution

It presents a novel phase field approach with anisotropic energy functionals to penalize overhangs, including rigorous mathematical analysis and numerical demonstrations.

Findings

Effective overhang penalization demonstrated in numerical tests

Mathematical derivation of optimality conditions for anisotropic energies

Connection established between phase field approach and sharp interface models

Abstract

A phase field approach for structural topology optimization with application to additive manufacturing is analyzed. The main novelty is the penalization of overhangs (regions of the design that require underlying support structures during construction) with anisotropic energy functionals. Convex and non-convex examples are provided, with the latter showcasing oscillatory behavior along the object boundary termed the dripping effect in the literature. We provide a rigorous mathematical analysis for the structural topology optimization problem with convex and non-continuously-differentiable anisotropies, deriving the first order necessary optimality condition using subdifferential calculus. Via formally matched asymptotic expansions we connect our approach with previous works in the literature based on a sharp interface shape optimization description. Finally, we present several numerical results to demonstrate the advantages of our proposed approach in penalizing overhang developments.