Sur le traitement des interfaces avec la méthode des éléments naturels

Aragon Institute of Engineering Research, University of Zaragoza, Spain
Francisco CHINESTA
Laboratoire de Mécanique des Systèmes et des Procédés (LMSP),
École Nationale Supérieure des Arts et Métiers (ENSAM), Paris

In this paper we address the problem of the numerical treatment of interphases in the framework of the Natural Element Method (NEM). This method, despite being considered meshless, presents several differences when compared to other meshless or meshfree methods. Noteworthy, the interpolant character of the approximation makes the imposition of essential and interphase boundary conditions straightforward, as in the FEM. In this paper we investigate the issue of imposing interphase boundary conditions when the model is constructed upon a suitable α-shape of the cloud of points. Α-shapes are an instance of shape constructors, geometrical entities that give a shape to a cloud of points with no boundary information. A particular highlight will be made in the problem of fluid-structure interactions, where the solid could possibly be modelled by finite elements, whereas the fluid is simulated by NE methods. The application to other problems involving evolving interphases (the so-called Stefan problems, for instance) will be also addressed.

Laboratoire de Mécanique des Structures et des Systèmes Couplés - LMSSC