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A node-to-node scheme for three-dimensional contact problems using the scaled boundary finite element method. (English) Zbl 1440.74251
Summary: A node-to-node (NTN) scheme for modeling three-dimensional contact problems within a scaled boundary finite element method (SBFEM) framework is proposed. Polyhedral elements with an arbitrary number of faces and nodes are constructed using the SBFEM. Only the boundary of the polyhedral element is discretized to accommodate a higher degree of flexibility in mesh transitioning. Nonmatching meshes can be simply converted into matching ones by appropriate node insertions, thereby allowing the use of a favorable NTN contact scheme. The general three-dimensional frictional contact is explicitly formulated as a mixed complementarity problem (MCP). The inherent nonlinearity in the three-dimensional friction condition is treated accurately without requiring piecewise linearization. Contact constraints for non-penetration and stick-slide are enforced directly in a complementarity format. Numerical examples with 1st and 2nd order elements demonstrate the accuracy and robustness of the proposed scheme.

MSC:
74M15 Contact in solid mechanics
74S05 Finite element methods applied to problems in solid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
Software:
FEAPpv; MCPLIB
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