Boundary Variational Inequality Approach in the Anisotropic Elasticity for the Signorini Problem
نویسندگان
چکیده
The purpose of the paper is reducing the three-dimensional Signorini problem to a variational inequality which occurs on the two-dimensional boundary of a domain occupied by an elastic anisotropic body. The uniqueness and existence theorems for the solution of the boundary variational inequality are proved and a boundary element procedure together with an abstract error estimate is described for the Galerkin numerical approximation. 2000 Mathematics Subject Classification: 35J85, 74B05.
منابع مشابه
A Direct Boundary Element Method for Signorini Problems
In this paper, a Signorini problem is reduced to a variational inequality on the boundary, and a direct boundary element method is presented for its solution. Furthermore, error estimates for the approximate solutions of Signorini problems are given. In addition, we show that the Signorini problem may be formulated as a saddle-point problem on the boundary.
متن کاملA VARIATIONAL APPROACH TO THE EXISTENCE OF INFINITELY MANY SOLUTIONS FOR DIFFERENCE EQUATIONS
The existence of infinitely many solutions for an anisotropic discrete non-linear problem with variable exponent according to p(k)–Laplacian operator with Dirichlet boundary value condition, under appropriate behaviors of the non-linear term, is investigated. The technical approach is based on a local minimum theorem for differentiable functionals due to Ricceri. We point out a theorem as a spe...
متن کاملNumerical analysis of a non-linear transmission problem with Signorini contact using dual-dual mixed-FEM and BEM — a priori and a posteriori error estimates
In this paper we generalize the approach in [5] and discuss an interface problem consisting of a non-linear partial differential equation in Ω ⊂ Rn (bounded, Lipschitz, n ≥ 2) and the Laplace equation in the unbounded exterior domain Ωc := R n\Ω̄ fulfilling some radiation condition, which are coupled by transmission conditions and Signorini conditions imposed on the interface. The interior pde i...
متن کاملFictitious Domain Formulation of Unilateral Problems
The fictitious domain method for the solution of variational inequalities with the Signorini boundary conditions is analyzed.
متن کاملSubstructuring of a Signorini-type problem and Robin's method for the Richards equation in heterogeneous soil
We prove a substructuring result for a variational inequality concerning — but not restricted to — the Richards equation in homogeneous soil and including boundary conditions of Signorini’s type. This generalizes existing results for the linear case and leads to interface conditions known from linear variational equalities: continuity of Dirichlet and flux values in a weak sense. In case of the...
متن کامل