On elastic waves in a medium with randomly distributed cylinders.
On the global solvability of a class of fourth-order nonlinear boundary value problems.
On the membrane approximation for thin elastic shells in the hyperbolic case.
We consider the variational formulation of the problem of elastic shells in the membrane approximation, when the medium surface is hyperbolic. It appears that the corresponding bilinear form behaves as some kind of two-dimensional elasticity without shear rigidity. This amounts to saying that the membrane behaves rather as a net made of elastic strings disposed along the asymptotic curves of the surface than as an elastic two-dimensional medium. The mathematical and physical reasons of this behavior...
On the solvability of a variational inequality problem and application to a problem of two membranes.
On the Unilateral Contact Between Membranes. Part 1: Finite Element Discretization and Mixed Reformulation
The contact between two membranes can be described by a system of variational inequalities, where the unknowns are the displacements of the membranes and the action of a membrane on the other one. We first perform the analysis of this system. We then propose a discretization, where the displacements are approximated by standard finite elements and the action by a local postprocessing. Such a discretization admits an equivalent mixed reformulation. We prove the well-posedness of the discrete problem...
Optimal control of variational inequality with applications to axisymmetric shells
The optimal control problem of variational inequality with applications to axisymmetric shells is discussed. First an existence result for the solution of the optimal control problem is given. Next is presented the formulation of first order necessary conditionas of optimality for the control problem governed by a variational inequality with its coefficients as control variables.
Optimal design of cylindrical shell with a rigid obstacle
The aim of the present paper is to study problems of optimal design in mechanics, whose variational form are inequalities expressing the principle of virtual power in its inequality form. We consider an optimal control problem in whixh the state of the system (involving an elliptic, linear symmetric operator, the coefficients of which are chosen as the design - control variables) is defined as the (unique) solution of stationary variational inequalities. The existence result proved in Section 1...
Optimization of the shape of axisymmetric shells
Axisymmetric thin elastic shells of constant thickness are considered and the meridian curves of their middle surfaces taken for the design variable. Admissible functions are smooth curves of a given length, which are uniformly bounded together with their first and second derivatives, and such that the shell contains a given volume. The loading consists of the hydrostatic pressure of a liquid, the shell's own weight and the internal or external pressure. As the cost functional, the integral of the...