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

We consider the case of thermal bending of linear elastic polygonal pl ates with simply supported edges and show that the deflections and ben ding moments according to the Reissner-Mindlin theory of moderately th ick plates are identical to the corresponding solutions of the Kirchho ff theory for thin plates. This is true far simply supported boundary conditions of the hard-hinged type. Imposed thermal moments may be arb itrarily distributed, and the plan view of the plate may be of an arbi trary polygonal shape. Furthermore, we show that the shearing forces o f such moderately thick plates vanish identically. This is in contrast to the results of the Kirchhoff theory, which predicts nonvanishing a nd possibly singular boundary reaction forces. Consequently, deflectio ns 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-call ed Kirchhoff-forces, should be omitted. The validity of this statement is demonstrated using finite-element as well as analytical solutions for rectangular and triangular plates. An erroneous analytical result from the literature for thermally stressed moderately thick rectangula r plates is resolved and corrected.