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Nonlinear elastic beam theory with application in contact problems and variational approaches. (English) Zbl 0843.73042
By considering the stress in lateral direction, a nonlinear beam theory is developed for large displacement and small strain. Application to the unilateral problem with obstacle is illustrated, and a nonlinear complementarity problem is proposed. We prove that this nonlinear complementarity problem is equivalent to a variational inequality.

MSC:
74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74A55 Theories of friction (tribology)
74M15 Contact in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
74P10 Optimization of other properties in solid mechanics
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