Upper and Lower Bounds for Deflections of Laminated Cantilever Beams Including the Effect of Transverse Shear Deformation

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Abstract
We state a method for obtaining upper and lower-bound results for the end deflection of a narrow rectangular cantilever beam, treated as a problem in plane stress. Reference is made to well-known earlier approximate results for this problem, using elementary polynomial solutions of Airy’s differential equation, and using approximate, rather than exact boundary conditions, without the establishment of bounds for the error in the approximate solution. Application of the bound method is here limited by the use of simple polynomial approximations for stresses and displacements, with the possibility remaining to obtain improved bounds by more elaborate choices of approximation functions.

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