Flexure Theory of Multi-Layer Orthotropic Circular Sandwich Plates

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Abstract
A small deflection theory is presented for the flexure of multi- layer orthotropic circular sandwich plates by extremizing the com plementary energy with the use of Lagrange multipliers. The strain energy is supplemented by the equations defining the stress re sultants and equilibrium in which each one is preceded by a different Lagrange multiplier. The Euler-Lagrange equations re sulting from the extremization process are then solved simul taneously with the equations of stress resultants and equilibrium to yield the governing equations. These equations are then used to solve several symmetrical cases and one non-symmetrical case, namely a simply supported plate with hydrostatic load. Curves are included to show the effect of shear and the degree of orthotropy on the deflection for several cases.

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