Plate on elastic foundation subject to thermal loading

The simplest and most widely used plate theory is the classical small deflection theory founded by Lagrange. This theory does not include the effect of temperature and any middle surface forces arising from the deformation of the plate are ignored. The problem of plates subject to temperature distribution are, however, of great practical importance and to treat this class of problems, a generalization of the Lagrange plate equation is necessary. The problem treated here is that of a circular plate resting on elastic foundation and subject to an arbitrary temperature distribution across its thickness and to uniform normal surface loading. (orig.)