The work presented here focuses on the reduction of computational effort associated with Robust Design Optimization (RDO) for crashworthiness of large industrial models. For the robust design study, the computational effort is determined by the following two aspects: (i) time for the computation of a single crash event and (ii) the number of evaluations required for the robustness of each design. For the first aspect, the possibility of using physical surrogate models (sub-structures or linear models obtained via the Equivalent Static Loads Method (ESLM)) to reduce the single simulation time is investigated. The sub-structuring approach is beneficial in situations where only a small part or sub-structure of a large complex structure has to be optimized to improve performance of the overall structure. ESLM generates the same deformation fields by linear static analysis as from the non-linear dynamic analysis and enables thereafter faster computations. Through these two approaches, the physical characteristics can still be represented sufficiently well even though the numerical effort for each design evaluation is reduced remarkably. The gain in computational time allows for the realization of a “true” robust design optimization, a so called double-loop approach, where in the optimization loop an additional loop is embedded for stochastic analysis to assess the robustness. This leads, in contrast to a single loop approach where robustness is only controlled at the end of the optimization, to optima under the robustness constraint. For the second aspect, a Modified Double Loop RDO (MDLRDO) approach has been implemented for the first time where the robustness analysis, through non-linear dynamic analysis, is only made for designs that are in a special Target Interval (TI). Robustness analysis, through non-linear dynamic analysis, is only made on special design points, which are both feasible and in a certain respect optimal(designs closer to the boundaries of the feasible design space). For the design points outside TI, robustness analysis is approximated through linear static analysis using ESLM. Through this approach the number of expensive non-linear dynamic analysis required in a RDO can be significantly reduced and large industrial problems can be optimized rarely achieved before. The three approaches, sub-structuring, ESLM and MDLRDO, have been successfully validated. In the next step these three approaches were combined to create an efficient robust design optimization loop. This approach is first applied to a robust design optimization problem considering uncertainties of thickness parameters only and is extended then to include variations in shape parameters and impact conditions.
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The work presented here focuses on the reduction of computational effort associated with Robust Design Optimization (RDO) for crashworthiness of large industrial models. For the robust design study, the computational effort is determined by the following two aspects: (i) time for the computation of a single crash event and (ii) the number of evaluations required for the robustness of each design. For the first aspect, the possibility of using physical surrogate models (sub-structures or linear m...
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