Variational formulation of a contact problem for linearly elastic and physically nonlinear shallow shells
The shell is described by a parametric equation of the form \(R=R(x_ 1,x_ 2)\in C^{(2)}(S)\), where S is a finite sum of bounded star domains. After shell deformation it is necessary to satisfy the condition \(f(R)+U\cdot \text{grad} f(R)\geq 0, \forall(x_ 1,x_ 2)\in S\), where \(U(x_ 1,x_ 2)\) is the displacement vector of the middle surface. For this thin shell in interaction with a smooth absolutely rigid stamp (without friction in the contact domain) a variational problem is analysed. Using the Sobolev space and the Lions-Stampachia method of variational inequalities this problem is reduced to a problem of a Lagrange functional. The existence and uniqueness conditions of the solution of this problem are established in this work.
Lions-Stampachia method of variational inequalities
scientific article; zbMATH DE number 3850622