VIRTUAL BOUNDARY ELEMENT-LINEAR COMPLEMENTARY EQUATIONS FOR SOLVING THE ELASTIC OBSTACLE PROBLEMS OF THIN-PLATE

A thin plate with arbitrary shape and arbitrary boundary conditions ha s gap delta(X) between the bottom surface of plate and the elastic win kler foundation. When the thin plate is subjected to the action of tra nsverse loads, the deflextion W(X) at point x will be obstructed by th e elastic foundation, if the deflection W(X)>delta(X). So the problem of finding W(X) is a nonlinear one. In this paper the theory of the vi rtual energy inequality equation and the virtual boundary element meth od (VBEM) are used to formulate a system of linear complementary equat ions under the condition that all boundary conditions are satisfied. T wo examples are solved numerically by Lemke algorithm. The results of one example coincide very well with that of the analytical solution wh ile delta(X)=0, and the results of the second example agree very well with the symmetrical conditions, because there is no analytical soluti on in this example. The advantages of this method are that there are n o singular integrals to be handled and the iterative calculation is to tally avoided. (C) 1997 Elsevier Science B.V.