Stresses in moderately thick rectangular plates
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By the use of recurrence relations the displacements, which satisfy the equilibrium equations, are expressed in terms if U0, V0, U1, V1, W0 and W1;The partial differential equations defining these six functions are obtained for any normal load which can be represented as a polynomial in x,y continuous over the entire plate;These equations are solved for the particular load P1+axa+ byb subject to three different sets of edge conditions: pinned-pinned, pinned-free, pinned-clamped;The results show that the principal part of the vertical displacement of the middle surface is W00, the corresponding thin plate solution. With the one exception noted in the previous chapter, the displacement of the middle surface is given as the thin plate solution plus a correction which is a function of the thin plate solution. Since the results depend upon W00, two thin plate solutions, not hitherto recorded, are given;The partial differential equations for the case of a shearing load are also given;It is shown that this method gives the problems of plane and generalized plane stress very easily.