A priori error for unilateral contact problems with Lagrange multipliers and isogeometric analysis

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. For the displacement, we use the pushforward of a NURBS space of degree p and for the Lagrange multiplier, the pushforward of a B-Spline space of degree p−2. These choices of space ensure to prove an inf−sup condition and so on, the stability of the method. We distinguish between contact and non-contact sets to avoid of classical geometrical hypothesis of the contact set. An optimal a priori error estimate is demonstrated without assumption on the unknown contact set. Several numerical examples in two- and three-dimensions and in small and large deformation demonstrate the accuracy of the proposed method.


Published in:
IMA Journal of Numerical Analysis, 39, 4, 1627-1651
Year:
2019
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 Record created 2018-05-01, last modified 2020-04-20

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