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Bi-Complementarity and Duality: A Framework in Nonlinear Equilibria with Applications to the Contact Problem of Elastoplastic Beam Theory

Authors
Journal
Journal of Mathematical Analysis and Applications
0022-247X
Publisher
Elsevier
Publication Date
Volume
221
Issue
2
Identifiers
DOI: 10.1006/jmaa.1998.5935
Keywords
  • Complementarity Problems
  • Duality
  • Variational Inequality
  • Nonsmooth Analysis
  • Contact Problem
  • Beam Theory

Abstract

Abstract Nonlinear complementarity problems and variational inequalities in nonlinear equilibrium problems are studied within a unified framework. Based on the generalized Rockafellar–Tonti diagram, a bi-complementarity problem with both internal and external nonlinear complementarity conditions is proposed. A general duality theory in variational inequality is established and the Mosco dual variational inequality has been generalized to the nonsmooth systems. In order to study the frictional contact problem of beam theory, a two-dimensional elastoplastic beam model is proposed. The external complementarity condition provides the free boundary of contact region, while the internal complementarity condition gives the interface of the elastic–plastic regions. Our results shown that in nonsmooth equilibrium problems, the dual approaches are much easier than the primal problems.

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