Arc-Length Method for Frictional Contact Problems Using Mathematical Programming with Complementarity Constraints

Y. Kanno and J. A. C. Martins
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Y. Kanno: The University of Tokyo
J. A. C. Martins: Departamento de Engenharia Civil e Arquitectura and ICIST

Journal of Optimization Theory and Applications, 2006, vol. 131, issue 1, No 6, 89-113

Abstract: Abstract A new formulation as well as a new solution technique is proposed for an equilibrium path-following method in two-dimensional quasistatic frictional contact problems. We consider the Coulomb friction law as well as a geometrical nonlinearity explicitly. Based on a criterion of maximum dissipation of energy, we propose a formulation as a mathematical program with complementarity constraints (MPEC) in order to avoid unloading solutions in which most contact candidate nodes become stuck. A regularization scheme for the MPEC is proposed, which can be solved by using a conventional nonlinear programming approach. The equilibrium paths of various structures are computed in cases such that there exist some limit points and/or infinite number of successive bifurcation points.

Keywords: Contact problems; Coulomb’s friction; arc-length method; mathematical program with complementarity constraints; maximum dissipation (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1007/s10957-006-9127-3

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