Yield and Buckling Stress Limits in Topology Optimization of Multiscale Structures

2025-05-07

AI Summary

This work addresses the challenge of concurrently optimizing strength and stability in multiscale structural topology optimization. We propose, for the first time, a unified framework that simultaneously couples material yield stress constraints with both local and global buckling constraints. Leveraging homogenization theory, we introduce a density-dependent von Mises yield surface model and define a yield load factor (YLF) to quantify strength capacity. Integrated with multilevel buckling mode analysis, this yields a YLF-driven multi-constraint optimization algorithm. Unlike conventional approaches focusing solely on stiffness or a single failure mode, our method enables synergistic strength–stability co-design. Numerical experiments demonstrate that optimized topologies are significantly influenced by the material stiffness-to-yield ratio; moreover, de-homogenized structures retain high predictive accuracy even on coarse meshes, confirming engineering applicability.

Technology Category

• Constraint Satisfaction and Optimization: Constraint Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

This study presents an extension of multiscale topology optimization by integrating both yield stress and local/global buckling considerations into the design process. Building upon established multiscale methodologies, we develop a new framework incorporating yield stress limits either as constraints or objectives alongside previously established local and global buckling constraints. This approach significantly refines the optimization process, ensuring that the resulting designs meet mechanical performance criteria and adhere to critical material yield constraints. First, we establish local density-dependent von Mises yield surfaces based on local yield estimates from homogenization-based analysis to predict the local yield limits of the homogenized materials. Then, these local Yield-based Load Factors (YLFs) are combined with local and global buckling criteria to obtain topology optimized designs that consider yield and buckling failure on all levels. This integration is crucial for the practical application of optimized structures in real-world scenarios, where material yield and stability behavior critically influence structural integrity and durability. Numerical examples demonstrate how optimized designs depend on the stiffness to yield ratio of the considered building material. Despite the foundational assumption of separation of scales, the de-homogenized structures, even at relatively coarse length scales, exhibit a high degree of agreement with the corresponding homogenized predictions.

Problem

• Integrate yield stress and buckling constraints in multiscale topology optimization
• Develop framework combining yield limits with local/global buckling criteria
• Ensure optimized designs meet mechanical performance and material yield constraints

Innovation

• Integrates yield stress and buckling constraints
• Uses density-dependent von Mises yield surfaces
• Combines local and global buckling criteria