Isogeometric analysis and shape optimal design of shell structures

Isogeometric analysis is a new method of computational analysis with the goal of merging design and analysis into one model by using a unified geometric representation. NURBS (Non-Uniform Rational B-Splines) are the most widespread technology in today’s CAD modeling tools and therefore are adopted as basis functions for analysis. In this thesis, the isogeometric concept is applied to the analysis and shape optimization of shell structures. A new, rotation-free shell element is developed, using the Kirchhoff-Love shell theory and NURBS as basis functions. NURBSbased analysis provides advantages especially for shells, since the structural behavior of a shell is mainly determined by its geometry and therefore a good geometric description is essential. Furthermore, due to the exact geometry description with NURBS, curvatures can be evaluated directly on the surface without rotational degrees of freedom or nodal directors. Different examples show the good performance and accuracy of the method, for geometrically linear and nonlinear problems. Aspects concerning boundary conditions and the treatment of multiple patch structures are investigated, and solutions are proposed which allow the use of this method for a broad variety of problems. Furthermore, the developed shell formulation proves as very well suited for a direct integration into a CAD model, which is also realized in a commercial CAD software. The practical application of this integrated method for different examples also reveals problems and limitations of the present approach, which are discussed subsequently. Another goal of this thesis is to extend the isogeometric concept to shape optimization. After a brief review of shape optimization using CAD-based or FE-based design models, isogeometric shape optimization is introduced as a combination of both existing approaches which enhances flexibility in choosing the design space. In the context of a cooperation project, the developed structural formulation is integrated into a fluid-structure interaction (FSI) environment and is applied to the three-dimensional FSI simulation of a wind turbine blade rotating in the air flow. This example shows the relevance of this method to large industrial applications.