Plate Analogy for the Torsion Problem

Abstract

An analogy between the bending of simply supported plates loaded by uniformly distributed edge moments and the torsion of prismatic bars is derived. The analogy is drawn for both straight‐sided and circularly curved boundaries. The method is extended to the case of hollow shafts. The analogy is demonstrated using analytical and the finite element methods for the rectangular, triangular, circular, hexagonal, semicircular, and hollow circular section. The method shows that excellent results can be obtained using the finite element plate analogy. The deviation between the plate analogy and classical solutions is less than 10% for the maximum shear stress evaluation and less than 13% for twist evaluations. The very wide‐spread availability of plate bending finite elements makes the plate analogy a pragmatic engineering solution technique, by which one operation can solve two different problems. The analogy offers a method of problem solution without the development, acquisition, and maintenance of additional software.