A level set based approach for the finite element simulation of a forming process involving multiphysics coupling: Ultrasonic welding of thermoplastic composites

International audienceThermoplastic composite materials o_er new perspective in the mechanical industry, especially in aeronautic. The assembly of huge structures by welding is made possible by the ability of the matrix to melt. This paper focuses on ultrasonic welding process where heating is con_ned at the welding interface.This is achieved thanks to a local mechanical dissipation in triangles specially located at the interface, called energy director. In order to better understand the phenomena that occur at the energy director scale, we propose to model and simulate the polymer ow at the interface. Based on a previous work, the ow under vibration is modeled using three coupled boundary value problems. A speci_c simulation tool is then developed for solving those three problems. It entails speci_c numerical methods: a level set method allows to handle the large geometry change, and an iterative solver manages the multiphysical aspects. The novel simulation obtained is validated with a qualitative comparison to experiments. Then, an analysis of the numerical results allows to understand the phenomena that enables welding. A thermomechanical localization heats the tip of the energy director. This initiates a fold of polymer, that progressively _lls the gap between the two plates to weld, and ensures conditions for adhesion

Hierarchic multigrid iteration strategy for the discontinuous Galerkin solution of the steady Euler equations

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High-order <i>h</i>-adaptive discontinuous Galerkin methods for ocean modelling

In this paper, we present an h-adaptive discontinuous Galerkin formulation of the shallow water equations. For a discontinuous Galerkin scheme using polynomials up to order p, the spatial error of discretization of the method can be shown to be of the order of hp+1, where h is the mesh spacing. It can be shown by rigorous error analysis that the discontinuous Galerkin method discretization error can be related to the amplitude of the inter-element jumps. Therefore, we use the information contained in jumps to build error metrics and size field. Results are presented for ocean modelling problems. A first experiment shows that the theoretical convergence rate is reached with the discontinuous Galerkin high-order h-adaptive method applied to the Stommel wind-driven gyre. A second experiment shows the propagation of an anticyclonic eddy in the Gulf of Mexico

High-order h-adaptive discontinuous Galerkin methods for ocean modeling

High-order h-adaptive Discontinuous Galerkin methods for ocean modelin