I³MS - Kiendl Seminar
Prof. Dr. Josef Kiendl - Isogeometric Methods in Structural Analysis
Isogeometric analysis is a recent method of computational analysis where functions used to describe geometries in Computer Aided Design (CAD) are adopted as basis for analysis. Due to this unified geometric representation, the model transfer from design to analysis, called mesh generation, is omitted providing a better integration of design and analysis. NURBS are the most widespread technology in today’s CAD modeling tools and therefore are adopted as basis functions for analysis. Apart from the geometrical advantages, NURBS-based isogeometric analysis has proven superior approximation properties compared to standard finite element analysis for many different applications. Furthermore, the high continuity between elements also allows the discretization of higher order PDEs, which is especially useful in structural mechanics, where the classical plate and shell theories, based on Kirchhoff’s kinematic assumption, can be implemented in a straightforward way.
We show an isogeometric shell analysis framework with formulations ranging from linear, geometrically nonlinear, and fully nonlinear shell models. All formulations are based on the Kirchhoff-Love shell theory and are rotation-free, i.e., using only displacement degrees of freedom. These formulations are then employed for the simulation of various problems of structural mechanics, including large deformations, buckling, elastoplasticity, and brittle fracture as well as for fluid-structure-interaction problems including the simulations of offshore wind turbine blades and bioprosthetic heart valves.
Furthermore, we show how the high continuity provided by IGA can be used in order to develop innovative structural models. In particular, we show formulations for shear deformable beams and plates with only one unknown variable, which is a generalized displacement. Corresponding numerical formulations are characterized by having considerably less degrees of freedoms than the standard formulations and are also fully locking-free.