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By P. R. Lancaster, D. Mitchell

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Extra resources for Advanced Solid Mechanics: Theory, worked examples and problems

Sample text

41 (b) A second set of boundary conditions is to let the vertical line at x = L, y = 0 remain vertical and again do not allow the point to move. Thus u at x and v =0 L, y = 0. 10g are very different in appearance because of the choice of boundary conditions. In these expressions only points defined by (x, y) in the plate can be used and statements regarding how the boundaries are fixed have to be carefully considered and analysed. 10g when x = 0 PL 3 vf = 3EI the usual formula derived from elementary theory.

6a. Hence the stresses are a = a = 0 and X y T = -c which represents a constant shear stress applied to a plate. xy (d) Thus ~ = ay 2 + cxy + bx 2 represents bi-axial stresses accompanied by shear stresses and it will be evident that quite complex problems can be examined using this semi-inverse method. 6) is always satisfied. 1 Stress Boundaries To solve the problem of an end loaded cantilever plate the direct approach will be given in detail ~ ~ ~ ,..... p __,. X L y Fig. 2 The force P acts over the free end of the plate and Ox represents the centroidal axis for the undeformed plate.

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