Multilayered shell theories accounting for layerwise mixed description, part 1: Governing equations

A Reissner mixed variational equation is employed in this paper to derive t he differential governing equations of multilayered, double curved shells m ade of orthotropic laminae in linear static cases. A layerwise description is referred to by assuming two independent fields in the thickness directio n for the transverse stress (both shear and normal components) and displace ment variables in each layer. Interlaminar values are used as the unknown v ariables of the introduced expansions. The continuity conditions of displac ements and transverse shear and normals stresses at the interfaces between two consecutive layers, referred to as C-z(0) requirements, have been a pri ori fulfilled, These have been used to drive the governing equations from a layer to a multilayered level. Classical displacement formulations and rel ated equivalent single-layer equations have been derived for comparison pur poses. 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 ot her available two-dimensional solutions are given in a companion paper (E. Carrera, "Multilayered shell Theories Accounting for Layerwise Mixed Descri ption, Part 2: Numerical Evaluations," AIAA Journal, Vol. 37, No. 9, 1999, pp. 1117-1124).