Nonlinear elastic beam theory with application in contact problems and variational approaches

Abstract

From the first equation we know that a: is a constant, so this beam model is actually a linear ordinary differential equation. If the beam is quite thick, the deformation in lateral direction can not be ignored. By considering the stress in lateral direction, a nonlinear beam theory is developed in this paper for large displacement and small strain elastic beam theory. Application to the unilateral problem with obstacle is illustrated and a nonlinear complementarity problem is proposed. We proved that this nonlinear complementarity problem is equivalent to a variational inequality and a primal variational approach.