A Comparison of Various Kinematic Models for Sandwich Shell Panels with Soft Core

Abstract

A large variety of classical and advanced shell theories are assessed in the present work to evaluate bending response of sandwich shell structures with soft core. The accuracy of classical, higher order, zig-zag, layer-wise, and mixed theories is compared in the case of closed form solutions of simply supported shell panels made by two external skins and an internal soft core. Thickness strain effects have been evaluated too. The various theories have been implemented in a compact and concise form by referring to Carrera’s unified formulation (CUF) for plate/shell analysis that has been, in the recent past, introduced by the first author. Shell theories accuracy has been established with respect to a geometrical parameter (length-to-thickness-ratio) and to a mechanical one (face-to-core-stiffness-ratio). Soft core cases have been mostly analyzed. Two main sources of error have been outlined, which are related to the geometrical parameter and to the mechanical one, respectively. It has been concluded that higher order theories (HOTs) can be conveniently used to reduce the error due to the geometrical parameter in thick shell cases. HOTs are instead not effective to increase the accuracy of classical theories analysis whenever the error is caused by increasing values of the mechanical parameter; layer-wise analysis becomes mandatory in this last case. Among the considered equivalent single layer theories, of particular interest are those zig-zag theories that make use of Murakami’s zig-zag function.