area of the plate. For the analysis we may conveniently employ the method of total potential energy since we have already, in Chapter 5, derived expressions for strain and potential energy corresponding to various load and support configurations. In these expressions we assumed that the displacement of the plate comprises bending deflections only and that these are small in comparison with the thickness of the plate. These restrictions therefore apply in the subsequent theory.

First we consider the relatively simple case of the thin plate of Fig. 6.14, loaded as shown, but simply supported along all four edges. We have seen in Chapter 5 that its true deflected shape may be represented by the infinite double trigonometrical series w

Also, the total potential energy of the plate is, from Eqs (5.37) and (5.45)

0 0

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