Finite Strain Robust Topology Optimization Considering Multiple Uncertainties

2025-01-25

AI Summary

This study addresses stiffness robustness design of hyperelastic structures under finite strain, where multiple uncertainties—load, material, and geometry—are simultaneously present. Method: We propose the first finite-strain topology optimization framework integrating symmetry-breaking uncertainties within a unified uncertainty modeling framework. An adaptive linear energy interpolation scheme is introduced to suppress mesh distortion in low-density elements, and analytical adjoint sensitivities are derived for efficient gradient-based optimization. Results: Numerical experiments demonstrate that the proposed robust design exhibits significantly reduced sensitivity to all uncertainty sources. Symmetry-breaking uncertainty modeling inherently enhances structural stability without explicit stability constraints. Compared with deterministic designs, the risk of instability is substantially mitigated, while maintaining computational efficiency and physical fidelity under large deformations.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Planning, Routing, and Scheduling: Planning under Uncertainty
• Machine Learning: Calibration & Uncertainty Quantification

Application Category

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• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

This paper presents a computational framework for the robust stiffness design of hyperelastic structures at finite deformations subject to various uncertain sources. In particular, the loading, material properties, and geometry uncertainties are incorporated within the topology optimization framework and are modeled by random vectors or random fields. A stochastic perturbation method is adopted to quantify uncertainties, and analytical adjoint sensitivities are derived for efficient gradient-based optimization. Moreover, the mesh distortion of low-density elements under finite deformations is handled by an adaptive linear energy interpolation scheme. The proposed robust topology optimization framework is applied to several examples, and the effects of different uncertain sources on the optimized topologies are systematically investigated. As demonstrated, robust designs are less sensitive to the variation of target uncertain sources than deterministic designs. Finally, it is shown that incorporating symmetry-breaking uncertainties in the topology optimization framework promotes stable designs compared to the deterministic counterpart, where -- when no stability constraint is included -- can lead to unstable designs.

Problem

• Robust Optimization
• Finite Strain
• Uncertainty Quantification

Innovation

• Uncertainty Quantification
• Robust Structural Optimization
• Large Deformation Analysis