By J. Haslinger (auth.), M. Raous, M. Jean, J. J. Moreau (eds.)
This complaints quantity includes sixty six papers offered on the moment "Contact Mechanics foreign Symposium" held in Carry-Le-Rouet. France. from September nineteenth to twenty third. 1994, attended through a hundred and ten members from 17 international locations. This symposium used to be the continuation of the 1st CMIS held in 1992 in Lausanne. of the Symposium Euromech 273 "Unilateral touch and Dry Friction" held in 1990 in los angeles Grande Motte. France. and of the sequence of "Meetings on Unilateral difficulties in Structural research" equipped in Italy. some other yr. through the eighties. the first goal of the symposium was once to convey experts of touch mechanics jointly as a way to draw a consultant photograph of the state-of-the-art and to spot new traits and new positive aspects within the box. In view of the contributions made. one may well assert that the mechanics of touch and friction has now reached a level the place the rules are transparent either from the mathematical and from the computational standpoints. many of the problems met could be pointed out through asserting that frictional touch is ruled via resistance legislation which are non soft and whose move rule isn't linked to the yield criterion in the course of the conventional normality property.
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Extra resources for Contact Mechanics
In this article, we focus on a general Signorini problem, corresponding to linearly elastic structures in unilateral contact with rigid and frictionless supports. The object desired from the design is a maximum of equilibrium potential energy. This well-known objective was treated as early as 1968 by Prager and Taylor and 1973 by Hemp. It is primarily, but not solely, a measure of structural stiffness. Design constraints will be presumed to consist of, at least, a so-called isoperimetric constraint, accounting for a fixed accessible amount of material.
1b). The expression of such nonfully determined laws in terms of nonconvex superpotentials permits the formulation of a variational theory for this class of problems. g. Feder (1991)). All these laws are nonmonotone - nonsmooth so it is difficult to incorporate the description of such laws into the standard formalism which usually operates only with simple functions. In the present work the basic idea for the mathematical description of these laws is the use of some fractal functions, the so called "fractal interpolation functions".
First the general assumptions and the state problem are dealt with. Then the structural optimization problem is treated in a general form. The objective functional is shown to yield, in a sense, small contact pressures and displacements, and the strain energy density will be evenly distributed. The design problem is identified with the dual problem connected to a saddle point in the potential energy as a function of displacement and design. The solvability of the design problem is shown from a saddle point theorem.