7.F2 v - Poisson's ratio, taken here to be 0.3 - total potential energy, given by U-W = JI VII.F.2: GENERAL REMARKS The differential equations governing the deformation of plates do not readily lend themselves to analytic solution in any but the simplest cases. Consequently, several approximate methods are used in solving practical plate bending problems. One of these is the Rayleigh-Ritz method which will be used here to determine the behavior of a stiffened square clamped plate subjected to a transverse pressure load. In this method (7.Fl) a displacement field is assumed in the form of a double sum of terms each consisting of an assumed mode shape and an undetermined amplitude coefficient. This displacement field is then used to compute the total potential energy of the plate and stiffeners, JI. Applic~tion of the Theorem of Minimum Potential Energy then defines the amplitude coefficients to provide an approximate representation of the plate deflections. This analysis will use a single term to approximate the displacement field in order to outline the basic procedure. Including many terms in the series increases the accuracy of the approximation, but also increases the computational difficulty of the problem. It is not the purpose of this report to draw up a detailed design of a Space Colony, rather the aim is to demonstrate the existence of the techniques necessary to accomplish such a design. VII.F.3 ANALYSIS Assume: Let f . (x) J. In the present analysis a b the Ritz polynomials 20m and a .. J.J
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