A Matlab code for analysis and topology optimization with Third Medium Contact

2025-11-28

AI Summary

Topology optimization of hyperelastic structures with contact boundaries remains challenging due to severe numerical instabilities arising from nonlinear contact mechanics and shear locking in low-density elements. Method: This work proposes an efficient numerical framework integrating the Third-Medium Contact (TMC) model with the Hu–Wu regularization strategy. The approach employs nonlinear finite element discretization, explicitly models contact mechanics via TMC, and applies Hu–Wu regularization to suppress shear locking in void regions—thereby enhancing robustness of nonlinear solution procedures—within a SIMP-based topology optimization loop. Contribution/Results: To the best of our knowledge, this is the first study to synergistically combine TMC and Hu–Wu regularization for hyperelastic contact-aware topology optimization. A compact, open-source MATLAB implementation is provided, supporting end-compliance minimization. Numerical experiments demonstrate stable convergence and reproducible results under strongly nonlinear contact conditions, while the framework exhibits promising extensibility to multiphysics problems.

Technology Category

• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems
• Systems and Infrastructure for Web, Mobile and WoT: Experiences and lessons learnt from Web-based algorithms and system deployments
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We present a Matlab code for modelling and topology optimization of hyperelastic structures, including contact modelled by the Third Medium Contact (TMC) approach. By using the so-called HuHu-regularization we penalize the skew distortion of the bilinear finite elements discretizing void regions, thus promoting convergence of the nonlinear solver. First, we show how this method is implemented in a compact code, allowing to simulate contact and force transfer in hyperelastic structures. Then, we solve a topology optimization problem for minimum end-compliance of a structure exhibiting contact. The Matlab scripts that replicate the results are included, and we discuss some possible extensions to more general problems.

Problem

• Develops a Matlab code for hyperelastic structures with contact modeling
• Implements topology optimization for minimum end-compliance in contact scenarios
• Uses HuHu-regularization to enhance solver convergence in void regions

Innovation

• Third Medium Contact for hyperelastic structures
• HuHu-regularization penalizes skew distortion
• Topology optimization for minimum end-compliance