SUMMARYThis paper is devoted to the imposition of Dirichlet-type conditions within the extended finite element method (X-FEM). This method allows one to easily model surfaces of discontinuity or domain boundaries on a mesh not necessarily conforming to these surfaces. Imposing Neumann boundary conditions on boundaries running through the elements is straightforward and does preserve the optimal rate of convergence of the background mesh (observed numerically in earlier papers). On the contrary, much less work has been devoted to Dirichlet boundary conditions for the X-FEM (or the limiting case of stiff boundary conditions). In this paper, we introduce a strategy to impose Dirichlet boundary conditions while preserving the optimal rate of convergence. The key aspect is the construction of the correct Lagrange multiplier space on the boundary. As an application, we suggest to use this new approach to impose precisely zero pressure on the moving resin front in resin transfer moulding (RTM) process while avoiding remeshing. The case of inner conditions is also discussed as well as two important practical cases: material interfaces and phase-transformation front capturing.
This paper deals with the slamming phenomenon for deformable structures. In a first part, a three-dimensional hydrodynamic problem is solved numerically with the Finite Element Method. The results for a rigid body are successfully compared to the analytical solutions.After the numerical analysis, an experimental investigation is presented. It consists in series of free fall drop-tests of rigid, deformable cones shaped models with different deadrise angle and thickness. Distribution of the pressure and its evolution are analyzed. Numerical and experimental results are compared and present good agreement.
This paper deals with slamming phenomenon (impact between bow ship and water free surface). Slamming loads on ship may be sufficiently important so as to create plastic deformations of the hull external structure. In extreme cases, they have been recognised for being responsible for the loss of ships. The problem to solve is transient and highly non-linear due to the character of the flow. In the present paper, the three-dimensional Wagner problem is solved numerically using a variational formulation together with a Finite Element Method. Three-dimensional results for simple rigid bodies such as a cone and an ellipsoid are successfully compared with analytical results. Results for deformable structure will be presented.
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