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Topology Optimization considering Shielding and Penetrating Features based on Fictitious Physical Model

Daiki Soma, Kota Sakai, Takayuki Yamada

TL;DR

This work tackles topology optimization with explicit geometric constraints by introducing shielding and penetrating features. It combines a level-set formulation with a fictitious steady-state temperature framework to evaluate these features, yielding objective terms that reward appropriate void-solid connectivity patterns. The method formulates a minimum mean compliance problem augmented by shielding and penetrating evaluators, solved with an augmented Lagrangian approach on 2D and 3D domains. Numerical demonstrations show the ability to form shielding walls and penetrating holes, with parameter studies guiding practical design choices for manufacturability and performance.

Abstract

This paper proposes topology optimization for considering shielding and penetrating features. Based on the fictitious physical model, which is a useful approach to control geometric features, the proposed method analyzes fictitious steady-state temperature fields and interprets target geometric features by examining the temperature change. First, the concept of topology optimization based on the level set method is introduced. Next, the basic idea of the fictitious physical model for considering geometric features is explained. Then, the differences between the shielding and penetrating features are clarified, and the fictitious physical model for evaluating these features is proposed. Furthermore, topology optimization for the minimum mean compliance problem with geometric conditions is formulated. Finally, 2D and 3D numerical examples are presented to validate the proposed method.

Topology Optimization considering Shielding and Penetrating Features based on Fictitious Physical Model

TL;DR

This work tackles topology optimization with explicit geometric constraints by introducing shielding and penetrating features. It combines a level-set formulation with a fictitious steady-state temperature framework to evaluate these features, yielding objective terms that reward appropriate void-solid connectivity patterns. The method formulates a minimum mean compliance problem augmented by shielding and penetrating evaluators, solved with an augmented Lagrangian approach on 2D and 3D domains. Numerical demonstrations show the ability to form shielding walls and penetrating holes, with parameter studies guiding practical design choices for manufacturability and performance.

Abstract

This paper proposes topology optimization for considering shielding and penetrating features. Based on the fictitious physical model, which is a useful approach to control geometric features, the proposed method analyzes fictitious steady-state temperature fields and interprets target geometric features by examining the temperature change. First, the concept of topology optimization based on the level set method is introduced. Next, the basic idea of the fictitious physical model for considering geometric features is explained. Then, the differences between the shielding and penetrating features are clarified, and the fictitious physical model for evaluating these features is proposed. Furthermore, topology optimization for the minimum mean compliance problem with geometric conditions is formulated. Finally, 2D and 3D numerical examples are presented to validate the proposed method.

Paper Structure

This paper contains 21 sections, 29 equations, 77 figures.

Table of Contents

  1. Introduction
  2. Conventional Approaches Adopted in This Paper
  3. Topology Optimization Based on Level Set Method
  4. Fictitious Physical Model for Geometric Feature Evaluation
  5. Evaluation of Target Geometric Feature
  6. Influence of Boundary Conditions
  7. Evaluation of Shielding Feature
  8. Evaluation of Penetrating Feature
  9. Application to Optimization Problem
  10. Formulation of Optimization Problem Considering Target Geometric Features
  11. Optimization Algorithm
  12. Numerical Examples
  13. Effect of Parameters on Shielding Feature
  14. 2D Example Under Shielding Condition
  15. 3D Example Under Shielding Condition
  16. ...and 6 more sections

Figures (77)

  • Figure 1: Definition of shielded and penetrated structures
  • Figure 2: Penetrated structure and specific cross-sections
  • Figure 3: Shielded structure and specific cross-sections
  • Figure 4: Problem setting for thermal analysis.
  • Figure 5: Distribution on cross-section 1-1 obtained from governing equation (\ref{['eq:GovDi']})
  • ...and 72 more figures