Finite Strain Robust Topology Optimization Considering Multiple Uncertainties

TL;DR

This paper develops a computational framework for robust topology optimization of hyperelastic structures under finite deformations, accounting for multiple uncertainties in loading, material, and geometry, leading to more stable and less sensitive designs.

Contribution

It introduces a stochastic perturbation method and adaptive energy interpolation to handle uncertainties and mesh distortion in finite strain topology optimization.

Findings

Robust designs are less sensitive to uncertainties than deterministic ones.

Incorporating symmetry-breaking uncertainties enhances design stability.

The framework effectively manages mesh distortion under large deformations.

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.