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A tenth-order theory of stretching of transversely isotropic sheets

Research paper by R. A. Clark, E. Reissner

Indexed on: 01 Nov '84Published on: 01 Nov '84Published in: Zeitschrift für angewandte Mathematik und Physik



Abstract

The problem of determining three-dimensional Poisson's ratio effect corrections for two-dimensional plane stress theory is solved approximately by assuming equilibrium stress systems with parabolic variations in thickness direction of the primary face-parallel stresses. An application of a variational theorem for stresses and displacements is shown to lead to a tenth-order system of two-dimensional differential equations for stress measures and certain weighted averages of displacements components. It is further shown that the solution of the tenth-order system can be expressed in terms of a bi-harmonic function, in conjunction with the solutions of one second-order and one fourth-order differential equation, involving Laplace operators only.