Michel Salaün

Study of Some Optimal XFEM Type Methods

The XFEM method in fracture mechanics is revisited. A first improvement is considered using an enlarged fixed enrichment subdomain around the crack tip and a bonding condition for the corresponding degrees of freedom. An efficient numerical integration rule is introduced for the nonsmooth enrichment functions. The lack of accuracy due to the transition layer between the enrichment aera and the rest of the domain leads to consider a pointwise matching condition at the boundary of the subdomain. An optimal numerical rate of convergence is then obtained using such a nonconformal method.

First vorticity-velocity-pressure numerical scheme for the Stokes problem

We consider the bidimensional Stokes problem for incompressible fluids and recall the vorticity, velocity and pressure variational formulation, which was previously proposed by one of the authors, and allows very general boundary conditions. We develop a natural implementation of this numerical method and we describe in this paper the numerical results we obtain. Moreover, we prove that the low degree numerical scheme we use is stable for Dirichlet boundary conditions on the vorticity. Numerical results are in accordance with the theoretical ones. In the general case of unstructured meshes, a stability problem is present for Dirichlet boundary conditions on the velocity, exactly as in the stream function-vorticity formulation. Finally, we show on some examples that we observe numerical convergence for regular meshes or embedded ones for Dirichlet boundary conditions on the velocity.

Two Dimensional Model of an Electro-Thermal Ice Protection System

In this communication we shall focus on the main governing equations and building blocks of the M.A.D (Anti-icing Deicing Modelling) numerical tool, which is now renamed as INUIT (Integrated NUmerical model of Ice protection sysTems) and part of the new generation of ONERA icing codes. The code simulates the functioning of an electro-thermal de-icing system. We shall also discuss the various improvements and new features we have added, especially a mechanical model of the ice block in order to improve the ice-shedding criterion.

An Eulerian approach for large displacements of thin shells including geometrical non-linearities

Abstract This paper is devoted to the problem of large displacement of shells, the only non-linearity being geometrical. The geometry of the mid-surface of the shell is determined thanks to the knowledge of nodes and normal vectors, and is continuously updated. Stresses are also carried from one configuration to another, which enables us to linearize the equilibrium equations. It is then possible to build an Eulerian formulation. Moreover, some control strategies are proposed, in order to find limit points and unstable solutions. Finally, we check in some classical examples, the accuracy of this technique.

Metal cutting modelling SPH approach

The purpose of this work is to evaluate the use of the smoothed particle hydrodynamics (SPH) method within the framework of high speed cutting modelling. First, a 2D SPH based model is carried out using the LS-DYNA® software. The developed SPH model proves its ability to account for continuous and shear localised chip formation and also correctly estimates the cutting forces, as illustrated in some orthogonal cutting examples. Then, the SPH model is used in order to improve the general understanding of machining with worn tools. At last, a hybrid milling model allowing the calculation of the 3D cutting forces is presented. The interest of the suggested approach is to be freed from classically needed machining tests: Those are replaced by 2D numerical tests using the SPH model. The developed approach proved its ability to model the 3D cutting forces in ball end milling.

Discrete harmonics for stream function-vorticity Stokes problem

Summary. We consider the bidimensional Stokes problem for incompressible fluids in stream function-vorticity. For this problem, the classical finite element method of degree one converges only in

A mixed finite element for shell model with free edge boundary conditions Part 3. Numerical aspects

\mathcal{O}(\sqrt{h})

Modelling Aeronautical Composite Laminates Behaviour under Impact Using a Saturation Damage and Delamination Continuous Material Model

for the

Discrete harmonics for the Stokes problem

L^2-

Some improvements of Xfem for cracked domains

norm of the vorticity. We propose to use harmonic functions to approach the vorticity along the boundary. Discrete harmonics are functions that are used in practice to derive a new numerical method. We prove that we obtain with this numerical scheme an error of order