Robust shape and topology optimization considering geometric uncertainties with stochastic level set perturbation

Abstract

When geometric uncertainties arising from manufacturing errors are comparable with the characteristic length or the product responses are sensitive to such uncertainties, the products of deterministic design cannot perform robustly. This paper presents a new level set-based framework for robust shape and topology optimization against geometric uncertainties. We first propose a stochastic level set perturbation model of uncertain topology/shape to characterize manufacturing errors in conjunction with Karhunen-Loève (K-L) expansion. We then utilize polynomial chaos expansion to implement the stochastic response analysis. In this context, the mathematical formulation of the considered robust shape and topology optimization problem is developed, and the adjoint-variable shape sensitivity scheme is derived. An advantage of this method is that relatively large shape variations and even topological changes can be accounted for with desired accuracy and efficiency. Numerical examples are given to demonstrate the validity of the present formulation and numerical techniques. In particular, this method is justified by the observations in minimum compliance problems, where slender bars vanish when the manufacturing errors become comparable with the characteristic length of the structures.

Topology optimization accounting for surface layer effects

“…The simple intuitive explanation is that for a topologically complicated structure, consisting of many structural members, the total length of the boundary is larger, resulting in more low stiffness material spent in the surface layer, working essentially like a perimeter constraint (Borrvall 2001). It can also be mentioned that similar trends have been observed in robust topology optimization considering uncertain geometrical boundary imperfections (Zhang and Kang 2017).…”

Current and future trends in topology optimization for additive manufacturing

“…In order to treat possible topoligical changes (e.g. breakage of structural members) caused by manufacturing errors in a mathematically more rigorous manner, Zhang and Kang [248] proposed a stochastic level set perturbation model of uncertain topology/shape to characterize manufacturing errors, and integrated this model with the random field-based uncertainty quantification techniques to achieve robust shape and topology optimization results. Recently, Keshavarzzadeh et al [249] presented a study on density-based topology optimization under manufacturing uncertainty by integrating the non-intrusive polynomial chaos expansion with design sensitivity analysis.…”

Robust topology optimization of phononic crystals with random field uncertainty

“…Robust topology optimization methods have been employed to generate robust structural configurations for uncertain external loads, [28][29][30][31] material distributions, [32][33][34] and geometrical shapes. [35][36][37] For instance, Jalalpour and Tootkaboni 38 presented a computationally efficient method for reliability-based topology optimization for continuum domains under material property uncertainty, where the response statistics are estimated with second-order stochastic perturbation. A robust topology optimization algorithm was also proposed by Changizi and Jalalpour 39 for frame structures under geometric or material uncertainties.…”