Topology optimization subject to additive manufacturing constraints

Moritz Ebeling-Rump,Robert Lasarzik,Dietmar Hömberg,Thomas Petzold

doi:10.1186/s13362-021-00115-6

Abstract

In topology optimization the goal is to find the ideal material distribution in a domain subject to external forces. The structure is optimal if it has the highest possible stiffness. A volume constraint ensures filigree structures, which are regulated via a Ginzburg–Landau term. During 3D printing overhangs lead to instabilities. As a remedy an additive manufacturing constraint is added to the cost functional. First order optimality conditions are derived using a formal Lagrangian approach. With an Allen-Cahn interface propagation the optimization problem is solved iteratively. At a low computational cost the additive manufacturing constraint brings about support structures, which can be fine tuned according to demands and increase stability during the printing process.

Highlights

Additive manufacturing or 3D printing is understood as the process of building up a structure layer by layer
The additive manufacturing constraint (AMC) was incorporated into the optimal control problem
Optimality conditions arose from a formal Lagrangian approach

Summary

Introduction

Additive manufacturing or 3D printing is understood as the process of building up a structure layer by layer. In the realm of optimization a smooth transition between material and void is desired in order to calculate derivatives This is achieved by explicitly allowing impure phases, i.e. states with 0 < φ < 1. Without limiting the material usage, the solution of the optimal control problem defined in Sect. This ensures that optimal solutions always have material placed where boundary forces act This minimization problem is not well-posed as explained in [3]. Following [2] the intermediate states are taken into consideration to ensure stability during manufacturing This can be thought of as slicing the final topology into horizontal layers and leads to the definition of the intermediate shape up to height h > 0 h := ∩ x = The results of the topology optimization depend on the following three parameters: the Ginzburg–Landau parameter , the Ginzburg–Landau term prefactor γ and AMC prefactor β

Parameter study for and γ

Findings

Conclusion