The analysis of a rotating circular plate is an easy problem because of circular symmetry. However, for the boundary other than circular, the problem will become much more complicated. For example, we may be theoretically interested in the stresses in a rectangular plate, which rotates with respect to its geometric center. If die thickness of he plate is small when compared with its length and width, the variation of stresses throughout the thickness can be neglected. Consequently, we shall have a two dimensional problem with body force acting. To solve a two dimensional problem with rectangular boundary is not always feasible. By using trigonometric series, we can only satisfy the conditions on the two sides of the plate. Accordingly the result can only be of value when the length of the plate is much larger than its width. If both dimensions of the plate are of the same order, the boundary conditions on the four sides must be considered. In the solution of the problem of this kind the principle of minimum strain energy may be successfully applied.
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