GREENS-FUNCTION APPROACH TO THE NONLINEAR BENDING OF CLOSELY-SPACED PARALLEL PLATES

This article presents a new extension of the Green's function method in computational mechanics. An iterative procedure is developed for analyzing the contact interaction in a system of closely-spaced parallel thin plates, possibly situated just above a Winkler foundation. The plates have uniform thicknesses and are composed of isotropic homogeneous elastic materials. Frictionless contact is also assumed. According to the classification proposed by Dundurs and Stippes (1970), the advancing contact has been discussed. The formulation of the problem brings a combination of two types of nonlinearities of different origins. The geometric nonlinearity resulting from relatively large deflections of the plates is accompanied by a nonlinearity which is due to the fact that the boundaries between contact and non-contact zones for each pair of plates are initially unknown. Linear problems appearing within each iteration are attacked by a version of the Green's function method. The technique utilizes the analytically constructed Green's functions and matrices for the biharmonic equation and Lame's system of the plane problem in the theory of elasticity. Contact conditions for each plate in the system are treated by implementing penalty functions. Numerical results are encouraging, and an extension of this study to more complicated formulations is currently under way.