Two-scale elastic shape optimization for additive manufacturing

TL;DR

This paper introduces a two-scale elastic shape optimization method for additive manufacturing, combining macro-scale free material optimization with micro-scale topology optimization, utilizing a precomputed database of realizable elasticity tensors.

Contribution

It presents a novel two-scale approach that integrates microscopic topology optimization with macro-scale free material optimization, optimized via a database and B-spline parametrization for additive manufacturing.

Findings

Efficient online macro-scale optimization using precomputed micro-scale data.

Database of realizable elasticity tensors with associated costs.

Effective incorporation of manufacturability constraints in microstructure design.

Abstract

In this paper, a two-scale approach for elastic shape optimization of fine-scale structures in additive manufacturing is investigated. To this end, a free material optimization is performed on the macro-scale using elasticity tensors in a set of microscopically realizable tensors. A database of these realizable tensors and their cost values is obtained with a shape and topology optimization on microscopic cells, working within a fixed set of elasticity tensors samples. This microscopic optimization takes into account manufacturability constraints via predefined material bridges to neighbouring cells at the faces of the microscopic fundamental cell. For the actual additive manufacturing on a chosen fine-scale, a piece-wise constant elasticity tensor ansatz on grid cells of a macroscopic mesh is applied. The macroscopic optimization is performed in an efficient online phase, whereas the associated cell-wise optimal material patterns are retrieved from the database that was computed offline. For that, the set of admissible realizable elasticity tensors is parametrized using tensor product cubic B-splines over the unit square matching the precomputed samples. This representation is then efficiently used in an interior point method for the free material optimization on the macro-scale.