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 has gap delta(X) between the bottom surface of plate and the elastic winkler foundation. When the thin plate is subjected to the action of transverse loads, the deflextion W(X) at point x will be obstructed by the 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 virtual energy inequality equation and the virtual boundary element method (VBEM) are used to formulate a system of linear complementary equations under the condition that all boundary conditions are satisfied. Two examples are solved numerically by Lemke algorithm. The results of one example coincide very well with that of the analytical solution while delta(X)=0, and the results of the second example agree very well with the symmetrical conditions, because there is no analytical solution in this example. The advantages of this method are that there are no singular integrals to be handled and the iterative calculation is totally avoided. (C) 1997 Elsevier Science B.V.