Reliability based bi-directional evolutionary topology optimization of geometric and material nonlinear analysis with imperfections

Abstract

This paper aims to present a novel computational technique for using reliability-based design while taking into account the effect of geometrically and materially nonlinear imperfect analysis. Consequently, a new bi-directional evolutionary structural optimization scheme is developed. A comparison is made between perfect geometrically and materially nonlinear analysis and imperfect geometrically and materially nonlinear analysis topology optimization designs for both deterministic and probabilistic analysis. In the case of probabilistic analysis, relevant parameters such as volume fraction (including manufacturing imprecisions), material properties, and geometrical imperfections (for stability calculations) are assumed to be random variables that follow a normal distribution to represent the uncertainties. The considered numerical examples have successfully illustrated that the proposed method can find the optimal topology for a reliability-based design using perfect geometrically and materially nonlinear analysis and imperfect geometrically and materially nonlinear analysis. Additionally, the results of the topology optimization according to the mean stress and the final optimized shapes have been influenced by introducing a reliability-based design, considering the reliability index as a bound governing the process.