Nonlinear elastic beam theory with application in contact problems and variational approaches. (English) Zbl 0843.73042

Gao, David Yang

Mech. Res. Commun. 23, No. 1, 11-17 (1996).

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

Keywords:

large displacement; small strain; unilateral problem with obstacle; nonlinear complementarity problem; variational inequality