A tenth-order theory of stretching of transversely isotropic sheets (Q1058334)

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 biharmonic function, in conjunction with the solutions of one second-order and one fourth-order differential equation, involving Laplace operators only.