Robust reliability-based topology optimization under random-field material model

TL;DR

This paper introduces a computationally efficient algorithm for topology optimization that accounts for material randomness, ensuring designs are both robust and reliable through probabilistic constraints and advanced stochastic methods.

Contribution

It develops a novel algorithm combining Karhunen-Loève expansion, sparse grid, and inverse-reliability techniques for robust, reliability-based topology optimization under random-field material models.

Findings

Validated on benchmark problems with Monte Carlo simulations.

Achieved computational efficiency through sparse grid and response surface methods.

Produced designs demonstrating improved robustness and reliability.

Abstract

This paper proposes an algorithm to find robust reliability-based topology optimized designs under a random-field material model. The initial design domain is made of linear elastic material whose property, i.e., Young's modulus, is modeled by a random field. To facilitate computation, the Karhunen-Lo\`eve expansion discretizes the modeling random field into a small number of random variables. Robustness is achieved by optimizing a weighted sum of mean and standard deviation of a quantity of interest, while reliability is employed through a probabilistic constraint. The Smolyak-type sparse grid and the stochastic response surface method are applied to reduce computational cost. Furthermore, an efficient inverse-reliability algorithm is utilized to decouple the double-loop structure of reliability analysis. The proposed algorithm is tested on two common benchmark problems in literature. Finally, Monte Carlo simulation is used to validate the claimed robustness and reliability of optimized designs.