Multilayered Shell Theories Accounting for Layerwise Mixed Description, Part 1: Governing Equations

Abstract

A Reissner mixed variational equation is employed in this paper to derive the differential governing equations of multilayered, double curved shells made of orthotropic laminae In linear static cases. A layerwise description is referred to by assuming two independent fields in the thickness direction for the transverse stress (both shear and normal components) and displacement variables in each layer. Interlaminar values are used as the unknown variables of the introduced expansions. The continuity conditions of displacements and transverse shear and normals stresses at the interfaces between two consecutive layers, referred to as C 0 z requirements, have been a priori fulfilled. These have been used to drive the governing equations from a layer to a multilayered level. Classical displacement formulations and related equivalent single-layer equations have been derived for comparison purposes. No assumptions have been made concerning the terms of type thickness to radii shell ratio h/R. Donnell's shallow shell-type equations are given as particular cases for all of the considered theories. Indicial notations and arrays have been used extensively to handle the presented developments in a concise manner. Numerical evaluations and comparisons to exact and other available two-dimensional solutions are given in a companion paper (E. Carrera, Multilayered Shell Theories Accounting for Layerwise Mixed Description, Part 2: Numerical Evaluations, AIAA Journal, Vol. 37, No. 9, 1999, pp. 1117-1124).