Méthodes numériques de représentation à variables séparées pour la résolution des problèmes paramétriques en mécanique non-linéaire des structures

摘要

The main purpose of this work is to propose a simulation method of thermomechanical transformations, well adapted to industrial or laboratory optimization problems. There is two different approaches: optimization by performing series of thermomechanical simulations while seeking the optimum, or optimization by response surface, which are built thanks to a set of simulations, before seeking the optimum. For these two approaches, we propose to exploit an adaptive reduced-order modeling method (APHR) allowing us to obtain simplified models which are sensitive to any model modifications (such as the variation of the parameters to optimize). The first approach consists in doing series of computations in process of optimization. We propose to complete the APHR method by managing the recurrent events appearing in different predictions. The principle of the proposed solution is to introduce a forgetting factor into the empirical modes definition. It has been illustrated on the identification of material parameters of damage model. The damage mechanisms relies on the Rousselier constitutive law. This forgetting factor enables us to improve the efficiency of the APHR method in the framework of inverse problems. With regard to optimization by response surface, we are only interested in the building of these response surfaces for sensitivity analysis. The originality of the developed approach lies in developing a numerical method based on separated representation of parametric problems: it's about performing simultaneously a set of multidimensional problems. This new approach has been illustrated by a sensitivity analysis of the response of a sintering model with respect to variation of material coefficients. The efficiency of the method has been proved by reducing the complexity of the problem.