Abstract
Formulas for upper and lower deflection bounds, in terms of appropriately applied approximations to potential and complementary energy expressions, are evaluated on the basis of variational problems which involve fourth-order ordinary Euler differential equations, with associated Euler and constraint boundary conditions. The paper obtains new information on the order of magnitude of effects which modify the results of elementary beam theory through the influence of transverse shear and normal strain deformations, including the delineation of boundary layer effects, with one or two such layers, depending on the degree of orthotropy of the material of the beam.
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