The Open Construction & Building Technology Journal

ISSN: 1874-8368 ― Volume 13, 2019

Geometry, Static, Vibration and Bucking Analysis and Applications to Thin Elliptic Paraboloid Shells

S.N. Krivoshapko1, G.L. Gbaguidi-Aisse2, *
1 RUDN University, 6, Miklukho-Maklaya Str, Moscow, 117198, Russia,
2 Laboratoire d'énergétique et de mécanique appliquées (LEMA) Ecole Polytechnique d'Abomey-Calavi/ Université d'Abomey-Calavi BP 2009 Cotonou, République du Bénin


A large number of references dealing with the geometry, static, vibration and buckling analysis of elliptic paraboloid shells exist in the literature. This review work attempts to organize and summarize the extensive published literature on the basic achievements in investigations of thin-walled structures in the form of elliptic paraboloids. Possibilities of elliptic paraboloids with reference to machine-building and construction designs and to the apparatuses used in theoretical physics are briefly considered. The geometric part of the review is extended due to consideration of optimization of surface’s sizes, researches of representation of a surface on the plane and introducing bibliographic material on fractal geometry. Several existent analytical and numeral methods of calculation of the examined shells on durability give a possibility to choose one of the methods for the solution of new two-dimensional or three-dimensional tasks. Geometrical researches, approximation and bending of elliptic paraboloid surfaces, research of the stress-strain state of shells by analytical and numerical methods, natural and forced vibration of a shell, forming and setting of surfaces, application of shells in the form of elliptic paraboloids are the main problems which are considered in this review.

Keywords: Application of elliptic paraboloid shells, Analytical and numerical methods of shell analysis, Elliptic paraboloid, Experimental methods of shell analysis, Grid system, Shell, Shell stability, Natural and forced vibrations.

Article Information

Identifiers and Pagination:

Year: 2016
Volume: 10
First Page: 576
Last Page: 602
Publisher Id: TOBCTJ-10-576
DOI: 10.2174/1874836801610010576

Article History:

Received Date: 18/06/2016
Revision Received Date: 31/10/2016
Acceptance Date: 19/11/2016
Electronic publication date: 19/12/2016
Collection year: 2016

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© Krivoshapko and Gbaguidi-Aisse; Licensee Bentham Open

open-access license: This is an open access article licensed under the terms of the Creative Commons Attribution-Non-Commercial 4.0 International Public License (CC BY-NC 4.0) (, which permits unrestricted, non-commercial use, distribution and reproduction in any medium, provided the work is properly cited.

* Address correspondence to this author at Laboratoire d'énergétique et de mécanique appliquées (LEMA) Ecole Polytechnique d'Abomey-Calavi/ Université d'Abomey-Calavi BP 2009 Cotonou, République du Benin; Tel: (229) 21300681; E-mail:


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