Isogeometric analysis of curved beams and thin shells

Abstract

New analysis tools must be developed in order to realize designs of increasing geometric complexity. The iterative work flow that is practiced between engineers and designers today is not fully sufficient. Reports from several industries state that 80% or more of analysis time is spent on converting Computer Aided Design (CAD) data to analysis suitable models. Besides being highly time-consuming, this procedure is also prone to generate errors. When going from CAD models to analysis models a change of discretization is performed which introduces geometrical approximations. Thus, a common platform for designers and engineers to work on is needed. A technique that stands out in its ability to truly integrate analysis with CAD is Isogeometric Analysis (IGA). It is a young approach in Finite Element Analysis (FEA) that utilizes the same mathematical basis for description as CAD technology, i.e. Non-Uniform Rational B-Splines (NURBS). In this thesis, the benefits and drawbacks of using IGA for integrated structural and architectural design are investigated. The question posed is whether IGA gives more accurate results and higher convergence rate than classic FEA on a per-degree-of-freedom basis. To this end, isogeometric analysis models based on Timoshenko and Euler-Bernoulli beam theory are implemented and the results are compared with results from classic FEA. Additionally, an isogeometric analysis model based on Kirchhoff-Love shell theory is implemented. For shells, the structural mechanics module of the finite element analysis software COMSOL MultiphysicsR, the software suite AbaqusTM and the programs ETABSR and RobotTM are used for comparing IGA with classic FEA.