Robust topology optimization design of structures with multiple load cases

In practical engineering, the structural performancealways exhibit some degree of variations due to the fact that the applied loadsfluctuate dramatically throughout its service life-cycle. Thus, the need ishighlighted to account for uncertainties in topology optimization stage ofthe structural design. Conventional deterministic topology optimizationsearches for minimum compliance without considering the uncertainties inoperating processes. Recently, the robust structural design has attractedintensive attentions because it can reduce the variability of structuralperformance. However, existing robust design methods are confined to thesize and shape optimization problems. This paper aims to incorporate therobust design strategy into the continuum topology optimization problemunder multiple uncertain load cases by minimizing variation of the objectiveperformance. Following the SIMP approach, an artificial isotropic materialmodel with penalization for elastic constants is assumed and elementalrelative density variables are used for describing the structural layout.The considered robust topology optimization problem is thus formulated as tofind the optimal structural topology that minimizes the standard deviationof structural total compliance under the constraint on material volume. Toavoid the difficulties associated with directly evaluating the standarddeviation of the structural compliance, a convenient computing formula ofthe objective function is presented based on the stochastic finite elementmethod. In addition, an adjoint variable method is employed for theefficient sensitivity analysis of the objective function. Then, the gradientbased optimization algorithm (Method of Moving Asymptotes, MMA) is used toupdate the design variables in the optimization loop. Finally, threenumerical examples for topology optimization of 2D and 3D structuresillustrate the applicability and the validity of the present model as wellas the proposed numerical techniques. The computational results reveal thatthe robust topology optimization could yield a material layout with lessvariation of structural compliance than the conventional deterministicapproach. The novelty of the proposed robust topology optimization approachlies in that it introduces the conception of robustness into earlier stageof the structural design, which may be considered as especial useful in somecircumstances.