Abstract
A variational formulation is proposed for the problem of thin shell interaction with a smooth absolutely rigid stamp without taking friction into account in the contact domain. The shell material can be linearly or nonlinearly elastic. (Elastic-plastic problem /1/ can be reduced to the latter case under certain assumptions). Application of the Lions—Stampachia method of variational inequalities reduces the task to the problem of minimizing a Lagrange functional in a set of allowable displacements. The existence and uniqueness of the solution are proved under definite assumptions about the properties of the strain diagram. Investigation of contact problems for finite size bodies by the Lions— Stampachia method of variational inequalities was executed in /2,3/. Problems on the bending of thin plates with unilaterial constraints were examined in /4/.
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