ON THERMAL BENDING OF MODERATELY THICK POLYGONAL PLATES WITH SIMPLY SUPPORTED EDGES

Abstract

We consider the case of thermal bending of linear elastic polygonal plates with simply supported edges and show that the deflections and bending moments according to the Reissner-Mindlin theory of moderately thick plates are identical to the corresponding solutions of the Kirchhoff theory for thin plates. This is true for simply supported boundary conditions of the hard-hinged type. Imposed thermal moments may be arbitrarily distributed, and the plan view of the plate may be of an arbitrary polygonal shape. Furthermore, we show that the shearing forces of such moderately thick plates vanish identically. This is in contrast to the results of the Kirchhoff theory, which predicts nonvanishing and possibly singular boundary reaction forces. Consequently, deflections and bending moments of the moderately thick plate can be calculated according to the simpler Kirchhoff theory for thin plates, while the results of the latter theory for boundary reaction forces, the so-called Kirchhoff-forces, should be omitted. ...