Mesh Morphing Methods for Virtual Prototyping and Mechanical Component Optimization

In this thesis, the coupling of mathematical geometry and its discretization (mesh) is performed using a method that fills the gap between simulation and design. Different modelling strategies are studied, tested and developed to bridge commercial CAD with a new methodology able to perform more accurate simulations without loosing the connection with the geometrical features. The aim of the thesis is to enhance the capabilities of Finite Element Methods (FEM) with the properties of Non-Uniform Radial Basis Functions (NURBS) inherited from CAD models in the design phase leading to a perfect representation of the model's boundary. The parametric space definition of the basis functions is borrowed from standard IGA (Isogeometric Analysis) and the possibility of process CAD models without the need for trivariate NURBS from NEFEM (NURBS Enhanced Finite Element Method). This particular combination yields to a bilinear Lagrangian basis and a new mapping between Cartesian and Parametric spaces for quadrilaterals. Using this new formulation it is possible to track the changes of the geometry and reduce the simulation's error up to 25-50% because of the perfect shape representation when compared to an equivalent FEM system. The problems presented are defined in a 2D space and solved using Matlab. NURBS are the key point to perform parametric morphing and simple optimizations while FEM remains the best way to perform simulations. This new method prevents to remodel B-Rep (Boundary Representation) parts after some simple modification due to the analysis and improves the geometry accuracy of the discretization. The geometrical file is directly imported from commercial software and processed by the method. Accuracy, convergence and seamless integration with commercial CAD packages are demonstrated applied to problems of arbitrary 2D geometry. The main problems treated are thermal analysis and solid mechanics where the better results are achieved.