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This and the next two images are from:
Andreas Apostolatos, Isogeometric analysis of thin-walled structures on multipatch surfaces in fluid-structure interaction”, PhD Thesis, Technical University of Munich, 2018
ABSTRACT: In this thesis, the Isogeometric Analysis (IGA) of thin-walled structures modelled by trimmed Non-Uniform Rational B-Spline (NURBS) multipatches and its application to partitioned Fluid-Structure Interaction (FSI) is detailed. The structural analysis spans from linear two-dimensional elasticity up to three-dimensional geometrically non-linear membrane and Kirchhoff-Love shell analysis. IGA is a modern numerical method for solving Boundary Value Problems (BVPs) which in contrast to the standard Finite Element Method (FEM) uses the exact geometric description of the problem. In the present work, special emphasis is put on the continuity of the solution between trimmed NURBS multipatch surfaces which are standard in Computer-Aided Design (CAD). In this way, no effort is spent in preparing the analysis model as opposed to meshing in standard FEM and smoother approximations of the unknown fields are enabled. The latter is critical for the approximation of problems with high variational index such as the Kirchhoff-Love shell problem. Additionally, surface coupled multi-physics problems such as FSI especially benefit from the smoothness of the solution provided by isogeometric structural analysis. Accordingly, Penalty, Lagrange Multipliers and Nitsche-type methods are detailed and elaborated for the multipatch coupling and the application of weak Dirichlet boundary conditions on such structural models. FSI simulation is of high importance for the prediction of the mutual interaction between a fluid flow and a flexible structure. Typically, the fluid and the structural problems are solved separately while the coupling conditions are satisfied in an iterative manner along their common interface. In this way, the independent use of suitable methods for the discretization of each physical field is enabled. To exploit the benefits of isogeometric structural analysis on multipatches in FSI, a novel isogeometric mortar-based mapping method for real world CAD geometries is elaborated and detailed. Accordingly, field transformations between low order discretized fluid surfaces and trimmed multipatch NURBS representations of the structural surfaces are enabled in order to satisfy the interface constraints. The thesis is complemented with numerical examples in a sequence of increasing complexity, thus extending isogeometric analysis of thin-walled structures on multipatch surfaces to multiphysics problems of the fluid-structure interaction type.
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