65N50 Mesh generation and refinement
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Document Type
- Doctoral Thesis (2)
Language
- English (2)
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Keywords
- ALE-Methode (1)
- B-Spline (1)
- B-splines (1)
- Fluid-Struktur-Kopplung (1)
- Gebietszerlegungsmethode (1)
- Gittererzeugung (1)
- Hyperelastizität (1)
- Isogeometrische Analyse (1)
- Level-Set-Methode (1)
- NURBS (1)
Faculty / Organisational entity
This thesis introduces a novel deformation method for computational meshes. It is based on the numerical path following for the equations of nonlinear elasticity. By employing a logarithmic variation of the neo-Hookean hyperelastic material law, the method guarantees that the mesh elements do not become inverted and remain well-shaped. In order to demonstrate the performance of the method, this thesis addresses two areas of active research in isogeometric analysis: volumetric domain parametrization and fluid-structure interaction. The former concerns itself with the construction of a parametrization for a given computational domain provided only a parametrization of the domain’s boundary. The proposed mesh deformation method gives rise to a novel solution approach to this problem. Within it, the domain parametrization is constructed as a deformed configuration of a simplified domain. In order to obtain the simplified domain, the boundary of the target domain is projected in the \(L^2\)-sense onto a coarse NURBS basis. Then, the Coons patch is applied to parametrize the simplified domain. As a range of 2D and 3D examples demonstrates, the mesh deformation approach is able to produce high-quality parametrizations for complex domains where many state-of-the-art methods either fail or become unstable and inefficient. In the context of fluid-structure interaction, the proposed mesh deformation method is applied to robustly update the computational mesh in situations when the fluid domain undergoes large deformations. In comparison to the state-of-the-art mesh update methods, it is able to handle larger deformations and does not result in an eventual reduction of mesh quality. The performance of the method is demonstrated on a classic 2D fluid-structure interaction benchmark reproduced by using an isogeometric partitioned solver with strong coupling.
We present a new efficient and robust algorithm for topology optimization of 3D cast parts. Special constraints are fulfilled to make possible the incorporation of a simulation of the casting process into the optimization: In order to keep track of the exact position of the boundary and to provide a full finite element model of the structure in each iteration, we use a twofold approach for the structural update. A level set function technique for boundary representation is combined with a new tetrahedral mesh generator for geometries specified by implicit boundary descriptions. Boundary conditions are mapped automatically onto the updated mesh. For sensitivity analysis, we employ the concept of the topological gradient. Modification of the level set function is reduced to efficient summation of several level set functions, and the finite element mesh is adapted to the modified structure in each iteration of the optimization process. We show that the resulting meshes are of high quality. A domain decomposition technique is used to keep the computational costs of remeshing low. The capabilities of our algorithm are demonstrated by industrial-scale optimization examples.