A Simple Matlab Code for Material Design Optimization Using Reduced Order Models

Area of Science:

• Computational Materials Science
• Mechanical Engineering
• Optimization Methods

Background:

• Topology optimization for material design with extreme properties is computationally intensive.
• The finite element method (FEM) is central to solving equilibrium equations, contributing significantly to computational cost.
• Model order reduction (MOR) techniques offer a pathway to mitigate these computational demands.

Purpose of the Study:

• To develop and present a simplified Matlab code for topology optimization in material design.
• To integrate and demonstrate three distinct MOR approaches within the topology optimization framework.
• To provide a complete, functional code for researchers and practitioners.

Main Methods:

• Topology optimization formulation for material design.
• Finite Element Method (FEM) for solving equilibrium equations.
• Implementation of three MOR approaches: Proper Orthogonal Decomposition (POD), on-the-fly reduced order model construction, and Approximate Reanalysis (AR).

Main Results:

• A functional Matlab code integrating topology optimization with three MOR techniques is successfully developed.
• The code facilitates the reduction of computational cost associated with solving equilibrium systems.
• Demonstration of POD, on-the-fly MOR, and AR within a practical material design context.

Conclusions:

• The presented Matlab code offers an efficient solution for topology optimization in material design.
• The integration of MOR techniques significantly reduces the computational burden of FEM-based simulations.
• The provided code serves as a valuable resource for advancing research in optimal material design.