New refined model for curved linear anisotropic rods with circular cross section

An asymptotic reduction method is introduced to construct a curved rod theory for a general anisotropic linearized elastic material. For the sake of simplicity, the cross section is assumed to be circular. The starting point is Taylor expansions about the mean-line in curvilinear coordinates, and th...

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Autores principales:	Erick Pruchnicki, Xiaoyi Chen, Hui-Hui Dai
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Curved rod theory Reduction method Anisotropic linearized elasticity Rod variational formulation Fourier series Classical rod theories Engineering (General). Civil engineering (General) TA1-2040
Acceso en línea:	https://doaj.org/article/ecf0caa08411433abf1b93c4ff663def
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spelling	oai:doaj.org-article:ecf0caa08411433abf1b93c4ff663def2021-12-01T05:06:04ZNew refined model for curved linear anisotropic rods with circular cross section2666-496810.1016/j.apples.2021.100046https://doaj.org/article/ecf0caa08411433abf1b93c4ff663def2021-06-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2666496821000121https://doaj.org/toc/2666-4968An asymptotic reduction method is introduced to construct a curved rod theory for a general anisotropic linearized elastic material. For the sake of simplicity, the cross section is assumed to be circular. The starting point is Taylor expansions about the mean-line in curvilinear coordinates, and the goal is to eliminate the two spatial variables in the cross section in a pointwise manner in order to obtain a closed system for the displacement coefficients. We achieve this by using a Fourier series for the lateral traction condition together with the use of cylindrical coordinates in the cross section and by considering exact tridimensional equilibrium equation. We get a closed differential system of ten vector unknowns, and after a reduction process we obtain a differential system of the vector of the mean line displacement and twist angle. Six boundary conditions at each edge are obtained from the edge term in the tridimensional virtual work principle, and a unidimensional virtual work principle is also deduced from the weak forms of the rod equations. Through one example, we show that our theory gives more accurate results than the ones of both classical Euler-Bernoulli rod theory and Timoshenko rod theory. The displacement field is computed for two types of material symmetry : isotropy and transverse isotropy.Erick PruchnickiXiaoyi ChenHui-Hui DaiElsevierarticleCurved rod theoryReduction methodAnisotropic linearized elasticityRod variational formulationFourier seriesClassical rod theoriesEngineering (General). Civil engineering (General)TA1-2040ENApplications in Engineering Science, Vol 6, Iss , Pp 100046- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Curved rod theory Reduction method Anisotropic linearized elasticity Rod variational formulation Fourier series Classical rod theories Engineering (General). Civil engineering (General) TA1-2040
spellingShingle	Curved rod theory Reduction method Anisotropic linearized elasticity Rod variational formulation Fourier series Classical rod theories Engineering (General). Civil engineering (General) TA1-2040 Erick Pruchnicki Xiaoyi Chen Hui-Hui Dai New refined model for curved linear anisotropic rods with circular cross section
description	An asymptotic reduction method is introduced to construct a curved rod theory for a general anisotropic linearized elastic material. For the sake of simplicity, the cross section is assumed to be circular. The starting point is Taylor expansions about the mean-line in curvilinear coordinates, and the goal is to eliminate the two spatial variables in the cross section in a pointwise manner in order to obtain a closed system for the displacement coefficients. We achieve this by using a Fourier series for the lateral traction condition together with the use of cylindrical coordinates in the cross section and by considering exact tridimensional equilibrium equation. We get a closed differential system of ten vector unknowns, and after a reduction process we obtain a differential system of the vector of the mean line displacement and twist angle. Six boundary conditions at each edge are obtained from the edge term in the tridimensional virtual work principle, and a unidimensional virtual work principle is also deduced from the weak forms of the rod equations. Through one example, we show that our theory gives more accurate results than the ones of both classical Euler-Bernoulli rod theory and Timoshenko rod theory. The displacement field is computed for two types of material symmetry : isotropy and transverse isotropy.
format	article
author	Erick Pruchnicki Xiaoyi Chen Hui-Hui Dai
author_facet	Erick Pruchnicki Xiaoyi Chen Hui-Hui Dai
author_sort	Erick Pruchnicki
title	New refined model for curved linear anisotropic rods with circular cross section
title_short	New refined model for curved linear anisotropic rods with circular cross section
title_full	New refined model for curved linear anisotropic rods with circular cross section
title_fullStr	New refined model for curved linear anisotropic rods with circular cross section
title_full_unstemmed	New refined model for curved linear anisotropic rods with circular cross section
title_sort	new refined model for curved linear anisotropic rods with circular cross section
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/ecf0caa08411433abf1b93c4ff663def
work_keys_str_mv	AT erickpruchnicki newrefinedmodelforcurvedlinearanisotropicrodswithcircularcrosssection AT xiaoyichen newrefinedmodelforcurvedlinearanisotropicrodswithcircularcrosssection AT huihuidai newrefinedmodelforcurvedlinearanisotropicrodswithcircularcrosssection
_version_	1718405576432549888

New refined model for curved linear anisotropic rods with circular cross section

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