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Limit analysis shape optimization for von Mises criterion
A. Maury.
Département de mathématiques et de statistique, Université Laval

Considering a structure made of a perfectly plastic material it is known that the stress problem is well posed as long as an admissible stress exists for the given loads $F$ . The goal of limit analysis is to compute $\lambda > 0 $ such that $\lambda F$ is the threshold load between the existence and the non-existence of a stress field.

From a mathematical point of view, the problem takes the form of a saddle point with respect to displacement $u$ and stress. For the von Mises yield function it is possible to write this problem as an infimum problem with respect to $u$ taken in BD since it can present surface discontinuities. Our goal is to perform a sensitivity analysis of $\lambda$ and compute the shape gradient. The non-uniquess of $u$ and its intrinsic lack of smoothness urge the use of a regularization. We choose the Norton-Hoff-Friaa regularisation which admits a unique solution $u_p$ which belongs to $W^{1,p}(\Omega)^d$ . We discuss the convergence of this model as $p$ tends to 1. Then, reformulating the problem with respect to $u_p$ into a saddle point problem, we compute the shape derivative and present some numerical experiments.

Date: 2018-07-24 à 12:00
Endroit: IFIP TC7 Conference on System Modelling and Optimization,Universität Duisburg-Essen, Essen (Allemagne)