Finite Twisting and Bending of Thin Rectangular Elastic Plates

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Abstract
An exact solution is obtained of the nonlinear equations for finite deflections of thin elastic plates, for a rectangular plate acted upon by twisting moments T and bending moments M simultaneously applied to two opposite edges of the plate. The principal results of the paper are relations between the moments T and M, on the one hand, and the angle of twist per unit of length θ, and the curvature k of the plate, on the other hand. These relations which are of the form T = T(θ, k) and M = M(θ, k) generalize previously known relations for the special cases for which either k = 0 or θ = 0. A numerical evaluation of the functions T(θ, k) and M(θ, k) reveals the existence of a characteristic jump phenomenon.

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