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Non-interior smoothing algorithm for frictional contact problems. (English) Zbl 1145.74424

Summary: A new algorithm for solving the three-dimensional elastic contact problem with friction is presented. The algorithm is a non-interior smoothing algorithm based on an NCP-function. The parametric variational principle and parametric quadratic programming method were applied to the analysis of three-dimensional frictional contact problem. The solution of the contact problem was finally reduced to a linear complementarity problem, which was reformulated as a system of nonsmooth equations via an NCP-function. A smoothing approximation to the nonsmooth equations was given by the aggregate function. A Newton method was used to solve the resulting smoothing nonlinear equations. The algorithm presented is easy to understand and implement. The reliability and efficiency of this algorithm are demonstrated both by the numerical experiments of LCP in mathematical way and the examples of contact problems in mechanics.

MSC:

74S30 Other numerical methods in solid mechanics (MSC2010)
74M15 Contact in solid mechanics
74M10 Friction in solid mechanics
90C20 Quadratic programming
90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
65K05 Numerical mathematical programming methods
90C90 Applications of mathematical programming
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