Engineering analysis with non conforming meshes and levelsets
(2016)
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- Authors
- Supervisors
- Remacle, Jean-FranƧois
- Abstract
- Finite element analyses became predominant in engineering offices to simulate the behaviour of parts to design. Yet the bottleneck of the method remains the mesh generation. This can be explained by the fact that the CAD representation of the geometry is not suited for a finite element simulation. It can include overlapping surfaces and small features unessential for the simulation. In this thesis, we present two new methods that attempt to limit human intervention in the meshing process. Both methods rely on an implicit representation of the geometry described by a levelset function, obtained as the signed distance function to the STL triangulation of the boundary of the geometry. An unstructured mesh surrounding the geometry is then generated wherein the boundaries are embedded. The first method is based on the cutting of the elements crossed by the embedded interface. Yet imposing Dirichlet boundary conditions with Lagrange multipliers on embedded interfaces creates an over-constrained problem that produces instabilities. To remove those instabilities, a Laplace stabilization term is introduced in the formulation. But this term includes a scalar stabilization coefficient that needs to be calibrated. The second method is based on local mesh adaptation in the vicinity of the embedded interface to obtain a nearly body-fitted mesh. Anisotropic mesh adaptation is required to obtain the geometrical convergence. The mesh size in the direction normal to the interface is imposed to obtain an optimal rate of convergence. The advantage of this method is that it is not intrusive. Finally, both methods are challenged on complex geometries in linear elasticity. Convergence and time of meshing and computation are analysed. Sensitive parameters are needed to perform the computation. This limits the robustness of both methods. Yet we believe that these contributions are a building block for the path towards the full automation of mesh generation.
- Affiliations
Citations
Bricteux, G. (2016). Engineering analysis with non conforming meshes and levelsets. https://hdl.handle.net/2078.5/80991