Component-wise reduced order model lattice-type structure design

TL;DR

This paper introduces a component-wise reduced order modeling approach for topology optimization of lattice structures, achieving significant speedups with minimal accuracy loss and enabling efficient design of lightweight, stiff structures.

Contribution

It proposes a novel component-wise reduced order model for topology optimization that drastically reduces computation time and allows reuse of training data across multiple design problems.

Findings

1000x speedup over full FEM models

Less than 1% relative error in solutions

Effective for designing lightweight, stiff lattice structures

Abstract

Lattice-type structures can provide a combination of stiffness with light weight that is desirable in a variety of applications. Design optimization of these structures must rely on approximations of the governing physics to render solution of a mathematical model feasible. In this paper, we propose a topology optimization (TO) formulation that approximates the governing physics using component-wise reduced order modeling, which can reduce solution time by multiple orders of magnitude over a full-order finite element model while providing a relative error in the solution of less than one percent. In addition, the offline training data set from such component-wise models is reusable, allowing its application to many design problems for only the cost of a single offline training phase, and the component-wise method is nearly embarrassingly parallel. We also show how the parameterization chosen in our optimization allows a simplification of the component-wise reduced order model (CWROM) not noted in previous literature, for further speedup of the optimization process. The sensitivity of the compliance with respect to the particular parameterization is derived solely in the component level. In numerical examples, we demonstrate a 1000x speedup over a full-order FEM model with relative error of less than one percent and show minimum compliance designs for two different cantilever beam examples, one smaller and one larger. Finally, error bounds for displacement field, compliance, and compliance sensitivity of the CWROM are derived.