Several Approximate Analyses of the Bending of a Rectangular Cantilever Plate by Uniform Normal Pressure

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Abstract
Three methods of approximating the deflections and moments occurring in a rectangular cantilever plate subjected to uniform normal pressure over its entire surface are presented in this paper. The first is the application of the well-known finite-difference procedure. The second and third are collocation methods, one based upon polynomial solutions of the Lagrange equation, the other employing “mixed” hyperbolic-trigonometric terms satisfying this equation. In the last two methods the boundary conditions are satisfied exactly along the clamped edge and at a finite number of points along the free edges of the plate. The results obtained for the particular case of a cantilever plate with uniform normal load indicate that the use of a relatively small number of points in the collocation method yields values of deflections and moments that are in substantial agreement with those given by the finite-difference procedure. It cannot be concluded from these results that the collocation method using the assumed functions will give satisfactory results with fewer points than the finite-difference method for cantilever plates with loading different from the one investigated.

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