Methods and guidelines for the choice of shell theories

Equivalent-Single-Layer discontinuous Galerkin methods for static analysis of multilayered shells

“…In fact, the study of the mechanical response of laminated shells is currently an active area of research, see e.g. [4,5,6,7].…”

“…Motivated by the need for more accurate models, researchers have therefore enriched the through-the-thickness assumptions and introduced the so-called higher-order theories for plate and shells, which can be classified into: Equivalent-Single-Layer (ESL) theories [15,16,17,18,19], whereby the layers are replaced by a single layer with equivalent mechanical properties, Layer-Wise (LW) theories [20,21,22,23,24,25], whereby each layer is treated independently, and sub-laminate theories [26], whereby groups of layers are replaced by groups of equivalent layers. A unified descriptions of these approaches has been introduced by the Carrera Unified Formulation (CUF) [27,28,29], which provides a framework able to determine the best 2D theory in terms of computational e ciency versus solution accuracy for a given structural problem [6]. Further approaches to the modelling of shell-like structures include the continuum-based solid-shell models [30], which are based on displacement degrees of freedom only, and the variable-kinematics models [31,32], where di↵erent structural theories are employed for di↵erent regions of the same structure.…”

Accurate Stress Analysis of Variable Angle Tow Shells by High-Order Equivalent-Single-Layer and Layer-Wise Finite Element Models

“…Cinefra and Carrera [ 23 ] performed linear analyses of composite cylindrical structures using finite shell elements with different through-the-thickness kinematics. A useful review of methods and guidelines for the choice of the shell model was reported by Petrolo and Carrera [ 24 ]. A detailed review of the theories is not within the scope of this work.…”

Accurate through-the-thickness stress distributions in thin-walled metallic structures subjected to large displacements and large rotations

“…Commercial codes adopt these classical theories [9,10] within their shell elements. As discussed by Petrolo and Carrera [11], it is important to process various parameters, for example, the anisotropy, gradients in the strain and stress fields, thickness ratio, and inhomogeneity to evaluate the accuracy of classical models. The applicability of the classical theories is limited to a narrow range of applications, for example, when dealing with the thinwalled structure and without local effects.…”

“…A review of the theories is not the scope of this work, but given the importance of the topic, a brief overview follows. Petrolo and Carrera [11] developed a useful review of methods and guidelines for the choice of shell theories. A parabolic distribution of transverse shear deformations across the thickness was considered by Reddy and Liu [12] in their shear model.…”