A priori error for unilateral contact problems with Lagrange multiplier and IsoGeometric Analysis
This work provides rigorous error bounds for contact problems in isogeometric analysis, benefiting computational mechanics researchers seeking reliable simulations.
The paper presents a theoretical analysis of unilateral contact problems using isogeometric analysis with Lagrange multipliers, proving inf-sup stability and optimal a priori error estimates without assumptions on the contact set. Numerical examples in 2D and 3D, small and large deformations, demonstrate accuracy.
In this paper, we consider unilateral contact problem without friction between a rigid body and deformable one in the framework of isogeometric analysis. We present the theoretical analysis of the mixed problem using an active-set strategy and for a primal space of NURBS of degree $p$ and $p-2$ for a dual space of B-Spline. A inf-sup stability is proved to ensure a good property of the method. An optimal a priori error estimate is demonstrated without assumption on the unknown contact set. Several numerical examples in two- and three-dimensional and in small and large deformation demonstrate the accuracy of the proposed method.