Robust topology optimization of thin plate structure under concentrated load with uncertain load position

Abstract

This study investigates the robust topology optimization of a thin plate structure under a concentrated load with load position uncertainty. The effect of uncertain load direction, load magnitude, and load distribution in topology optimization problems has been investigated in previous research, but few studies have dealt with robust topology optimization considering load position uncertainty. In this study, load position uncertainty is modeled using the convex hull model, in which the load position uncertainty is confined within a circular area whose center is at the nominal load position. The worst load condition is defined as that when the applied load is at a position in the convex hull that gives the worst value of the mean compliance. Here, the robust objective function is formulated as a weighted sum of the mean compliance obtained from the mean load condition and the worst compliance obtained from the worst load condition, with a plate model based on Reissner-Mindlin plate theory. The robust topology optimization problem is formulated using a level set-based topology optimization method. Through numerical examples, robust optimum configurations are compared with deterministic optimum configurations and the validity of the proposed robust design method is then discussed.

Robust topology optimization under load position uncertainty

“…The topology optimization problem under investigation is to find out an optimal solution of the material layout design that minimizes the structural compliance subject to a material volume constraint. Herein, the structure is subjected to an external load, which is not applied at a fixed position but acts in a bounded region along the boundary without a certain probability distribution . Usually, we choose the compliance C as the design objective function to gain a maximum stiffness of the structure.…”

“…Besides, during the whole service lifetime of a practical structure, an external applied load may experience changes or variations, to a certain extent, in its application situation because of the complicated loading environments . Thus, the optimal solutions and the associated structural performances obtained on the deterministic loading situations cannot be ensured to be still best or even better under the uncertain loading conditions . It is therefore very important as well as critical to take these uncertainties into account from the beginning of a structural design.…”

“…For the past decades, structural topology optimization problems with consideration of load uncertainties have received increasing interests in the design optimization community. Thus far, a variety of approaches and techniques have been proposed to characterize the uncertain loadings in their various aspects, and a comprehensive study of the associated problems under the load magnitude and/or direction uncertainties has been made in the literature . Usually, these loading uncertainties are assumed as the uncertain‐but‐bounded design parameters, and then the optimal design problem is expressed to minimize the worst objective function induced by the uncertain loading conditions (worst‐case method).…”

“…18,19 Thus, the optimal solutions and the associated structural performances obtained on the deterministic loading situations cannot be ensured to be still best or even better under the uncertain loading conditions. 10,[16][17][18][19][20] It is therefore very important as well as critical to take these uncertainties into account from the beginning of a structural design. Accordingly, the topology or layout optimization is required to suitably incorporate these load uncertainties into the preliminary optimal design process of a structure.…”

A consideration on robust design optimization problem through formulation of multiobjective optimization

“…This is due to the fact that the tradeoff relationship and the effects of uncertainty on the robust optimum design are not evaluated by the weighted sum approach. For example, it has been observed that the robust topology optimum design is quite similar to the deterministic optimum design in a certain load case [Nakazawa et al, 2016]. However, as the study used a weighted sum approach, the effect of uncertainty was not clarified in detail.…”