Topology optimization improves buckling analysis with adaptive eigenvalue counting
Topology optimization with buckling constraints: Adaptive eigenvalue aggregation and modality identification
Computational Engineering, Finance, and Science
Summary
When designing structures to avoid buckling, it is hard to know how many important stability modes to consider. The paper shows that fixing this number arbitrarily can cause errors or slow calculations. The authors introduce a method that automatically picks the right number of modes during design, saving time and keeping accuracy. They also create a way to understand how these modes combine in optimized designs, helping engineers better predict failure patterns.
What this means in practice
- •For structural engineers: Improve design accuracy and efficiency by dynamically identifying stability modes during topology optimization with buckling considerations.
- •For mechanical design teams: Predict complex buckled shapes in optimized components to guide reinforcement and material placement.
Authors
Badvelu Pranay Prabha, Prabhat Kumar
Abstract
This paper presents novel approaches to tackle two key challenges in topology optimization problems with buckling constraints: determining how many eigenvalues to aggregate and identifying the eigenvalue modality at the optimal design. We demonstrate the mathematical inconsistencies that arise when choosing an arbitrary fixed number of eigenvalues for aggregation. Specifically, if the multiplicity of the critical eigenvalues is smaller than the chosen subset size, coalescence with higher-order eigenvalues can occur. Neglecting these during aggregation causes incorrect sensitivities, while simply increasing the preselected eigenvalue count unnecessarily raises computational costs. To resolve this issue, we propose an approach that dynamically determines the exact number of eigenvalues required at each optimization iteration. The proposed approach reduces computation time significantly while maintaining competitive performance relative to the conventional method across the numerical experiments presented. Additionally, accurately predicting modality at the optimal point is crucial for understanding the buckled mode shapes of optimized designs. A new optimization formulation is proposed using the difference between eigenvalues to capture the true eigenvalue modality. This formulation is first validated on a classical 1D clamped column, successfully predicting both the bimodal solution and the optimal eigenvectors. The approach demonstrates that the optimal solutions for the wall reinforcement and shear-loaded hinged plate problems for the given set of parameters are trimodal and tetramodal, respectively.