Robust topology optimization of structures under uncertain propagation of imprecise stochastic-based uncertain field

TL;DR

This paper presents a new robust topology optimization framework that accounts for imprecise stochastic uncertainties in structural analysis, providing bounds on compliance and optimized layouts, validated through numerical examples.

Contribution

The study extends the Karhunen-Loève expansion and introduces an interval sensitivity analysis method for robust topology optimization under imprecise stochastic fields.

Findings

The proposed method accurately bounds compliance statistics.

It effectively handles imprecise random field uncertainties.

Numerical examples demonstrate its feasibility and accuracy.

Abstract

This study introduces a novel computational framework for Robust Topology Optimization (RTO) considering imprecise random field parameters. Unlike the worst-case approach, the present method provides upper and lower bounds for the mean and standard deviation of compliance as well as the optimized topological layouts of a structure for various scenarios. In the proposed approach, the imprecise random field variables are determined utilizing parameterized p-boxes with different confidence intervals. The Karhunen-Lo\`eve (K-L) expansion is extended to provide a spectral description of the imprecise random field. The linear superposition method in conjunction with a linear combination of orthogonal functions is employed to obtain explicit mathematical expressions for the first and second order statistical moments of the structural compliance. Then, an interval sensitivity analysis is carried out, applying the Orthogonal Similarity Transformation (OST) method with the boundaries of each of the intermediate variable searched efficiently at every iteration using a Combinatorial Approach (CA). Finally, the validity, accuracy, and applicability of the work are rigorously checked by comparing the outputs of the proposed approach with those obtained using the particle swarm optimization (PSO) and Quasi-Monte-Carlo Simulation (QMCS) methods. Three different numerical examples with imprecise random field loads are presented to show the effectiveness and feasibility of the study.