Abstract
Plate problems involving free edges have been historically difficult to solve, particularly when two free edges are adjacent, resulting in a free corner. The cantilevered square plate subjected to a transverse loading is one such problem for which an exact solution has not been achieved. In the present paper results obtained by various approximate methods are presented for this problem for the case of a uniform loading. Solutions obtained by the authors using the technique of point matching and the Rayleigh-Ritz method are compared with previously published finite-difference and experimental results and with Bernoulli-Euler beam and plane-strain approaches. Numerical results for deflections, slope components, bending and twisting moments, and transverse distributed shears are presented for a relatively fine gridwork of points on the plate boundary and within the interior. The anticlastic curvature is exhibited by all methods except beam theory. All methods present the interesting conclusion that the free edge deflection is greater when the plate is treated as a plate rather than a beam.
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