Yield and Buckling Stress Limits in Topology Optimization of Multiscale Structures

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.