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A primal–dual active set strategy for nonlinear multibody contact problems. (English) Zbl 1093.74056

Summary: Non-conforming domain decomposition methods provide a powerful tool for the numerical approximation of partial differential equations. For the discretization of a nonlinear multibody contact problem, we use the mortar approach with a dual Lagrange multiplier space. To handle the nonlinearity of the contact conditions, we apply a primal-dual active set strategy to find the actual contact zone. The algorithm can be easily generalized to multibody contact problems. A suitable basis transformation guarantees the same algebraic structure in the multibody situation as in the one body case. Using an inexact primal-dual active set strategy in combination with a multigrid method yields an efficient iterative solver. Different numerical examples for one and multibody contact problems illustrate the performance of the method.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74M15 Contact in solid mechanics
74B05 Classical linear elasticity

Software:

UG
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References:

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