Three-dimensional topology optimization of auxetic metamaterial using isogeometric analysis and model order reduction

TL;DR

This paper introduces a computationally efficient method for designing 3D auxetic metamaterials using isogeometric analysis combined with model order reduction, enabling effective topology optimization of micro-structures.

Contribution

It integrates isogeometric analysis with a level set-based topology optimization and employs reduced order modeling to significantly improve computational efficiency.

Findings

Effective design of 3D auxetic metamaterials demonstrated

Reduced computational time with model order reduction

Successful application in 2D and 3D numerical examples

Abstract

In this work, we present an efficiently computational approach for designing material micro-structures by means of topology optimization. The central idea relies on using the isogeometric analysis integrated with the parameterized level set function for numerical homogenization, sensitivity calculation and optimization of the effective elastic properties. Design variables, which are level set values associated with control points, are updated from the optimizer and represent the geometry of the unit cell. We further improve the computational efficiency in each iteration by employing reduced order modeling when solving linear systems of the equilibrium equations. We construct a reduced basis by reusing computed solutions from previous optimization steps, and a much smaller linear system of equations is solved on the reduced basis. Two- and three-dimensional numerical results show the effectiveness of the topology optimization algorithm coupled with the reduced basis approach in designing metamaterials.