Mathematical optimization of a plate volume under a p-Laplace partial differential equation constraint by using standard software


  • G Scharrer
  • S Volkwein
  • T Heubrandtner



A main aspect in the design of passenger cars with respect to pedestrian safety is the energy absorption capability of the engine hood. Besides that, the hood has to fulfill several other requirements. That makes it necessary to develop easy and fast to solve prediction models with little loss in accuracy for optimization purpose. Current simulation tools combined with standard optimization software are not well suited to deal with the above mentioned needs. The present paper shows the application of mathematical methods on a simplified self developed model to reduce the optimization effort. A linear and a nonlinear model are introduced and a way for solving both is pointed out. Finally it is shown, that it is possible to simplify models and get optimization results much faster by using mathematical theory. Such results can be used in support of the original problem or as an input to space mapping based optimization algorithms, such as surrogate optimization.


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How to Cite

Scharrer, G., Volkwein, S. and Heubrandtner, T. (2010) “Mathematical optimization of a plate volume under a p-Laplace partial differential equation constraint by using standard software”, The International Journal of Multiphysics, 4(1), pp. 1-10. doi: 10.1260/1750-9548.4.1.1.