Stress and strain recovery of laminated composite doubly-curved shells and panels using higher-order formulations Erasmo Viola 1,a , Francesco Tornabene 1,b , and Nicholas Fantuzzi 1,c DICAM Department, University of Bologna, Viale del Risorgimento 2, 40136 Bologna, Italy a erasmo.viola@unibo.it, b francesco.tornabene@unibo.it, c nicholas.fantuzzi@unibo.it Keywords: Doubly-Curved Shells, Higher-Order Equivalent-Single-Layer Theory, Composite Lami- nates, Generalized Differential Quadrature. Abstract. The present paper investigates the static behaviour of doubly-curved laminated compos- ite shells and panels. A two dimensional Higher-order Equivalent Single Layer approach, based on the Carrera Unified Formulation (CUF), is proposed. The differential geometry is used for the ge- ometric description of shells and panels. The numerical solution is calculated using the generalized differential quadrature method. The through-the-thickness strains and stresses are computed using a three dimensional stress recovery procedure based on the shell equilibrium equations. Sandwich pan- els are considered with soft cores. The numerical results are compared with the ones obtained with a finite element code. The proposed higher-order formulations can be used for solving elastic problems involved in the first stage of any scientific procedure of analysis and design of masonry structures. Introduction In the present paper a mechanical model based on the Carrera Unified Formulation (CUF) [1, 2] is presented. This general approach is valid for all types of structural modelling, e.g. doubly-curved, singly-curved and degenerate shells (plates, walls), and can be used both for the static and dynamic analyses of the structures at issue. A two-dimensional elastic theory will be considered. Introducing the Differential Geometry (DG) [3, 4] a generic shell mid-surface can be easily represented. The shell equilibrium equations depend also on the Lam´ e parameters A 1 (α 1 ,α 2 ), A 2 (α 1 ,α 2 ) and the radii of curvature R 1 (α 1 ,α 2 ), R 2 (α 1 ,α 2 ) that are defined by the position vector of the points laying on the middle shell surface. The present kinematic model is expanded for both in-plane and out-of-plane displacements, such as in [5]. Moreover, the zig-zag effect (Murakami's function) has been included. In the following, the Generalized Differential Quadrature (GDQ) method [6-8] is used to study the static behaviour of doubly-curved sandwich structures. Furthermore, a stress recovery procedure is implemented to evaluate the quantities through the shell thickness. It is worth mentioning that the stress recovery of the three dimensional displacements and of the strain and stress tensors for moderately thick structures is not fully detailed in literature. This paper exploits the CUF approach to the static analysis of deep multi-layered shells and panels within the initial curvature effect. It should be cited that the same procedure used in this paper has been successfully applied to arbitrarily shaped models [9-14]. The main novelty of the paper is discussed in the final section where the through-the-thickness stresses are reported for curved structures and compared to the ones solved by FEM. It is worth noting that, when the linear elastic behavior is supposed, the method proposed in this paper is capable of computing the six components of the stress tensor at any point of elements belonging to plane masonry structures [15-22], laminated cylindrical shells and panels [23-24], as well as masonry arches, vaults and domes [25-30]. In addition, it should be pointed out that elastic analysis is the first valuable tool for the structures in hand, especially before any repair or strengthening [31-36]. Theoretical approach The geometrical description of the shell structures and the handling of the fundamental system of equations of the present paper follow the previous work by the authors [2, 37-39] . Here, the differential Key Engineering Materials Vol. 624 (2015) pp 205-213 © (2015) Trans Tech Publications, Switzerland doi:10.4028/www.scientific.net/KEM.624.205 All rights reserved. No part of contents of this paper may be reproduced or transmitted in any form or by any means without the written permission of TTP, www.ttp.net. (ID: 137.204.150.20, University of Bologna, Bologna, Italy-30/07/14,13:01:05)