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Analysis of the Bending of a Uniformly Loaded Rectangular Plate with Variable Width Corner Supports

The bending of a rectangular elastic plate under uniform distributed load and simply supported at the corners by equal-leg angles is studied analytically. The width of the supporting legs can be varied symmetrically about the plate axes giving mixed boundary conditions with supported and free edges. The solution is set up by using the Le'vy–Na'dai approach and the mixed boundary equation at the edges are written in the form of dual series equations. By choosing the proper finite integral transform, the dual series equations can be written as a system of inhomogeneous Fredholm integral equations. The inhomogeneous Fredholm integral equations are reduced to a set of inhomogeneous algebraic simultaneous equations by using Simpson's rule and solved by Picard iteration. The deflection along the middle line of the rectangular plate with various lengths of simple support legs has been calculated.