Title: Using Fourier and Taylor series expansion in semi-analytical deformation analysis of thick-walled isotropic and wound composite structures
Authors: Jiran, Lukáš
Mareš, Tomáš
Citation: Applied and Computational Mechanics. 2016, vol. 10, no. 1, p. 27-48.
Issue Date: 2016
Publisher: University of West Bohemia
Document type: článek
URI: http://www.kme.zcu.cz/acm/acm/article/view/288
ISSN: 1802-680X (Print)
2336-1182 (Online)
Keywords: silnostěnná trubice;Fourierova řada;Taylorova řada;analytická metoda;deformační analýza
Keywords in different language: thick-walled tube;Fourier series;Taylor series;analytic method;deformation analysis
Abstract: Thick-walled tubes made from isotropic and anisotropic materials are subjected to an internal pressure while the semi-analytical method is employed to investigate their elastic deformations. The contribution and novelty of this method is that it works universally for different loads, different boundary conditions, and different geometry of analyzed structures. Moreover, even when composite material is considered, the method requires no simplistic assumptions. The method uses a curvilinear tensor calculus and it works with the analytical expression of the total potential energy while the unknown displacement functions are approximated by using appropriate series expansion. Fourier and Taylor series expansion are involved into analysis in which they are tested and compared. The main potential of the proposed method is in analyses of wound composite structures when a simple description of the geometry is made in a curvilinear coordinate system while material properties are described in their inherent Cartesian coordinate system. Validations of the introduced semi-analytical method are performed by comparing results with those obtained from three-dimensional finite element analysis (FEA). Calculations with Fourier series expansion show noticeable disagreement with results from the finite element model because Fourier series expansion is not able to capture the course of radial deformation. Therefore, it can be used only for rough estimations of a shape after deformation. On the other hand, the semi-analytical method with Fourier Taylor series expansion works very well for both types of material. Its predictions of deformations are reliable and widely exploitable.
Rights: © 2016 University of West Bohemia. All rights reserved.
Appears in Collections:Volume 10, number 1 (2016)
Volume 10, number 1 (2016)

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Please use this identifier to cite or link to this item: http://hdl.handle.net/11025/21634

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