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Static Analysis of Anisotropic Doubly-Curved Shell Subjected to Concentrated Loads Employing Higher Order Layer-Wise Theories

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 this Special Issue: Theoretical and Computational Modeling of Advanced Materials and Structures)

Computer Modeling in Engineering & Sciences 2023, 134(2), 1393-1468.

Received 28 February 2022; Accepted 26 April 2022; Issue published 31 August 2022


In the present manuscript, a Layer-Wise (LW) generalized model is proposed for the linear static analysis of doublycurved shells constrained with general boundary conditions under the influence of concentrated and surface loads. The unknown field variable is modelled employing polynomials of various orders, each of them defined within each layer of the structure. As a particular case of the LW model, an Equivalent Single Layer (ESL) formulation is derived too. Different approaches are outlined for the assessment of external forces, as well as for non-conventional constraints. The doubly-curved shell is composed by superimposed generally anisotropic laminae, each of them characterized by an arbitrary orientation. The fundamental governing equations are derived starting from an orthogonal set of principal coordinates. Furthermore, generalized blending functions account for the distortion of the physical domain. The implementation of the fundamental governing equations is performed by means of the Generalized Differential Quadrature (GDQ) method, whereas the numerical integrations are computed employing the Generalized Integral Quadrature (GIQ) method. In the post-processing phase, an effective procedure is adopted for the reconstruction of stress and strain through-the-thickness distributions based on the exact fulfillment of three-dimensional equilibrium equations. A series of systematic investigations are performed in which the static response of structures with various curvatures and lamination schemes, calculated by the present methodology, have been successfully compared to those ones obtained from refined finite element three-dimensional simulations. Even though the present LW approach accounts for a two-dimensional assessment of the structural problem, it is capable of well predicting the three-dimensional response of structures with different characteristics, taking into account a reduced computational cost and pretending to be a valid alternative to widespread numerical implementations.


Concentrated load; doubly-curved shells; generalized differential quadrature; laminated anisotropic materials; layer-wise theory; mapping technique

Cite This Article

Tornabene, F., Viscoti, M., Dimitri, R. (2023). Static Analysis of Anisotropic Doubly-Curved Shell Subjected to Concentrated Loads Employing Higher Order Layer-Wise Theories. CMES-Computer Modeling in Engineering & Sciences, 134(2), 1393–1468.

This work is licensed under a Creative Commons Attribution 4.0 International License , which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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