Efficient sensitivity analysis based on finite element model reduction

The computation of frequency and modeshape sensitivities with respect to design parameters is essential to many structural optimization and finite element update algorithms who use this gradient information to orient the search for a minimum of various objective functions. Sensitivity computations may often become prohibitively expensive if large-dimensional models are used. On the other hand, approximating the gradients may lead to poor estimates and a loss of convergence. The cost of Nelson's exact method to compute modeshape sensitivities is generally not acceptable for industrial size models. The present study thus gives a general categorization of existing approximation methods with suggestions for some new extensions. Iterative corrections of the sensitivities significantly improve the accuracy of predictions found using Fox and Kapoor's modal based sensitivities but still require the computation of the exact modes at the current design point. Fixed basis model reduction allow an extremely fast and relatively accurate prediction of both modeshapes and their sensitivities over a limited area of the parameter space. Illustrations using a 7980 DOF engine block model are provided to demonstrate the applicability of the proposed approaches while giving indications on their cost and accuracy for a model of realistic size.