Strong Formulation: A Powerful Way for Solving Doubly Curved Shell Structures

A theoretical framework based on an Equivalent Single Layer (ESL) approach is proposed in this chapter to develop several Higher-order Shear Deformation Theories (HSDTs) in a unified and compact manner. In particular, the maximum order of kinematic expansion can be arbitrarily chosen in order to define more refined displacement fields. The Murakami’s function can be also included in the model to take into account the so-called zig-zag effect. The proposed theory is employed to describe the mechanical behavior of doubly-curved shell structures made of composite materials. In particular, the differential geometry is used to define accurately the curved surfaces at issue. The strong formulation of the governing equation is solved by means of a numerical approach based on the Generalized Differential Quadrature (GDQ) method. The accuracy of both the theoretical model and the numerical method is shown through some applications, in which the solutions are compared with the results obtained by means of a three-dimensional finite element model.