SOLVABILITY THEORY AND PROJECTION METHODS FOR A CLASS OF SINGULAR VARIATIONAL-INEQUALITIES - ELASTOSTATIC UNILATERAL CONTACT APPLICATIONS

The mathematical modeling of engineering structures containing members capable of transmitting only certain type of stresses or subjected to noninterpenetration conditions along their boundaries leads generally to variational inequalities of the form (P) u is an element of C: [Mu - q, v - u] greater than or equal to 0, For All v is an element of C, where C is a closed convex set of R-N (kinematically admissible set), q is an element of R-N (loading strain vector), and M is an element o f R-NxN (stiffness matrix). If rigid body displacements and rotations cannot be excluded from these applications, then the resulting matrix M is singular and serious mathematical difficulties occur. The aim of this paper is to discuss the existence and the numerical computation o f the solutions of problem (P) for the class of cocoercive matrices. O ur theoretical results are applied to two concrete engineering problem s: the unilateral cantilever problem and the elastic stamp problem.