A point to segment contact formulation for isogeometric, NURBS based finite elements

Formulation of isogeometric finite elements has received a great deal of attention in the recent past. The present study deals with the treatment of problems in structural mechanics including large elastic deformations and contact. One decisive difference between isogeometric finite elements, based on NURBS functions and standard finite elements (FE), based on Lagrange polynomials, is higher inter-element continuity. This is a promising characteristics to model contact problems, as all issues associated with kinks between elements are naturally avoided. Particularly in cases with large sliding this has the potential to be an attractive feature. We present a bilateral isogeometric collocation contact formulation for geometrically non-linear two-dimensional problems, using Greville and Botella points to collocate the contact integrals. Different methods to obtain accurate and physically meaningful stress distributions are investigated and compared. The results show that the higher inter-element continuity, in context of non-smooth problems, may imply undesired effects in the numerical solution such as unphysical stress oscillations. Similar effects have been observed in standard p-FEM. Numerical experiments indicate that these oscillations may be avoided if the basis functions of contact and non-contact zones are separated by knot relocation and knot repetition.

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