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ARTICLE
Static Analysis of Doubly-Curved Shell Structures of Smart Materials and Arbitrary Shape Subjected to General Loads Employing Higher Order Theories and Generalized Differential Quadrature Method
Francesco Tornabene*, Matteo Viscoti, Rossana Dimitri
Department of Innovation Engineering, School of Engineering, University of Salento, Lecce, 73100, Italy
* Corresponding Author: Francesco Tornabene. Email:
(This article belongs to the Special Issue: Theoretical and Computational Modeling of Advanced Materials and Structures)
Computer Modeling in Engineering & Sciences 2022, 133(3), 719-798. https://doi.org/10.32604/cmes.2022.022210
Received 28 February 2022; Accepted 11 May 2022; Issue published 03 August 2022
Abstract
The article proposes an Equivalent Single Layer (ESL) formulation for the linear static analysis of arbitrarily-shaped
shell structures subjected to general surface loads and boundary conditions. A parametrization of the physical
domain is provided by employing a set of curvilinear principal coordinates. The generalized blending methodology
accounts for a distortion of the structure so that disparate geometries can be considered. Each layer of the stacking
sequence has an arbitrary orientation and is modelled as a generally anisotropic continuum. In addition, re-entrant
auxetic three-dimensional honeycomb cells with soft-core behaviour are considered in the model. The unknown
variables are described employing a generalized displacement field and pre-determined through-the-thickness
functions assessed in a unified formulation. Then, a weak assessment of the structural problem accounts for shape
functions defined with an isogeometric approach starting from the computational grid. A generalized methodology
has been proposed to define two-dimensional distributions of static surface loads. In the same way, boundary
conditions with three-dimensional features are implemented along the shell edges employing linear springs. The
fundamental relations are obtained from the stationary configuration of the total potential energy, and they are
numerically tackled by employing the Generalized Differential Quadrature (GDQ) method, accounting for nonuniform computational grids. In the post-processing stage, an equilibrium-based recovery procedure allows the
determination of the three-dimensional dispersion of the kinematic and static quantities. Some case studies have
been presented, and a successful benchmark of different structural responses has been performed with respect to
various refined theories.
Graphical Abstract
Keywords
Cite This Article
Tornabene, F., Viscoti, M., Dimitri, R. (2022). Static Analysis of Doubly-Curved Shell Structures of Smart Materials and Arbitrary Shape Subjected to General Loads Employing Higher Order Theories and Generalized Differential Quadrature Method.
CMES-Computer Modeling in Engineering & Sciences, 133(3), 719–798. https://doi.org/10.32604/cmes.2022.022210