Simulation of buckling in thin-walled structures using isogeometric analysis (IGA)

With the ever increasing complexity of products and the demand for faster development, numerical simulations of structural problems are an increasingly important tool in the preparation, reduction and even elimination of physical testing of structures.

MSc student: Thomas Haartsen
Daily supervisors: Dr. ir. J.J.C. Remmers, Dr. ir. C.V. Verhoosel
Project supervisor: Prof.dr.ir 
M.G.D. Geers

Thin-walled structures (shells and plates) constitute a special class of structures. These type of structures are encountered everywhere in industry (aviation, construction, civil engineering, maritime engineering etc.). The failure of such a structure is typically determined by its buckling behavior, with buckling usually occurring long before plastic failure. This is why we attempt to simulate buckling.

The mathematical framework used to describe the mechanics of shells involves second order derivatives of displacements which poses a problem when the traditional FEM would be used. Rotational degrees of freedom have to be added for example in order to solve the problem. With Isogeometric Analysis, which is based on NURBS, a very straightforward discretization is possible due to the higher-order differentiable basis functions. 

Since IGA uses the same basis functions as the geometry representation for the analysis, the analysis geometry is exact. This is a particular advantage for shell structures since these are very sensitive to geometric imperfections. Moreover, there is no need to perform a meshing operation from the design geometry to the analysis geometry, saving time and computational cost.