Robust topology optimization under load position uncertainty

Abstract

Summary The topology optimization problem of a continuum structure on the compliance minimization objective is investigated under consideration of the external load uncertainty in its application position with a nonprobabilistic approach. The load position is defined as the uncertain‐but‐bounded parameter and is represented by an interval variable with a nominal application point. The structural compliance due to the load position deviation is formulated with the quadratic Taylor series expansion. As a result, the objective gradient information to the topological variables can be evaluated efficiently in a quadratic expression. Based on the maximum design sensitivity value, which corresponds to the most sensitive compliance to the uncertain loading position, a single‐level optimization approach is suggested by using a popular gradient‐based optimality criteria method. The proposed optimization scheme is performed to gain the robust topology optimizations of three benchmark examples, and the final configuration designs are compared comprehensively with the conventional topology optimizations under the loading point fixation. It can be observed that the present method can provide remarkably different material layouts with auxiliary components to accommodate the load position disturbances. The numerical results of the representative examples also show that the structural performances of the robust topology optimizations appear less sensitive to the load position perturbations than the traditional designs.

Robust topology optimization under multiple independent uncertainties of loading positions

“…n e is the number of the elements involved in the applied load location variation taking simultaneously, for example, a distributed surface load across several elements. Moreover, the second‐order derivative the nominal compliance can also be evaluated as follows 30,33 where ∂{ u } e /∂ s i is the derivative of the nodal displacement vector of an element to a loading position variation.…”

“…However, few attempts had ever been made to incorporate this aspect of the external load uncertainties in the TO literature. Recently, the present authors studied the RTO of a continuum structure with consideration of the position uncertainty of an external load 30 . It appears that the uncertainty characteristics of a loading position may induce an acute impact on the final material layout of a structure.…”

“…Besides, some auxiliary members or load paths are also set up by redistribution of the available material resource within the design domain for effectively transferring the external load to the foundations once it is applied out of the prespecified position. Therefore, the robust structural TO solution looks quite different from the equivalent deterministic topology optimization (DTO) upon the loading point fixation, and the structural performance becomes more immune or insensitive to the loading position uncertainty 30 . The motivation behind this work is to expand the previous study of one uncertain load into multiple external loads of independent position uncertainties under the material volume constraint and then, explore the structural behavior variations, which are sometimes not intuitively understandable, under the loading point stochastic perturbations.…”

“…In this work, the RTO problem of a continuum structure is investigated still following the optimization scheme proposed in the authors' previous study 30 . The optimal material layout is gained by using the non‐probabilistic approach for the purpose of the compliance minimization.…”

“…Thereafter, a new technique is developed to integrate multiple independent loading position uncertainties into the optimization procedure in Section 5. It will be seen that when multiple loading uncertainties are involved, the option of the minimum (largest absolute) design sensitivity becomes arduous in comparison with only considering a load position uncertainty 30 . But the critical loading positions can still be identified by a QP optimization algorithm.…”