Get 20M+ Full-Text Papers For Less Than $1.50/day. Start a 14-Day Trial for You or Your Team.

Learn More →

Micropolar curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models

Micropolar curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models AbstractNew models for micropolar plane curved rods have been developed. 2-D theory is developed from general 2-D equations of linear micropolar elasticity using a special curvilinear system of coordinates related to the middle line of the rod and special hypothesis based on assumptions that take into account the fact that the rod is thin.High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First stress and strain tensors,vectors of displacements and rotation and body force shave been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate.Thereby all equations of elasticity including Hooke’s law have been transformed to the corresponding equations for Fourier coefficients. Then in the same way as in the theory of elasticity, system of differential equations in term of displacements and boundary conditions for Fourier coefficients have been obtained. The Timoshenko’s and Euler-Bernoulli theories are based on the classical hypothesis and 2-D equations of linear micropolar elasticity in a special curvilinear system. The obtained equations can be used to calculate stress-strain and to model thin walled structures in macro, micro and nano scale when taking in to account micropolar couple stress and rotation effects. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Curved and Layered Structures de Gruyter

Micropolar curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models

Zozulya, V.V.
Curved and Layered Structures , Volume 4 (1): 15 – Jan 26, 2017
Download PDF
15 pages

Loading next page...
 
/lp/de-gruyter/micropolar-curved-rods-2-d-high-order-timoshenko-s-and-euler-bernoulli-e5sPvjT7rs

References (80)

Publisher
de Gruyter
Copyright
© 2017
eISSN
2353-7396
DOI
10.1515/cls-2017-0008
Publisher site
See Article on Publisher Site

Abstract

AbstractNew models for micropolar plane curved rods have been developed. 2-D theory is developed from general 2-D equations of linear micropolar elasticity using a special curvilinear system of coordinates related to the middle line of the rod and special hypothesis based on assumptions that take into account the fact that the rod is thin.High order theory is based on the expansion of the equations of the theory of elasticity into Fourier series in terms of Legendre polynomials. First stress and strain tensors,vectors of displacements and rotation and body force shave been expanded into Fourier series in terms of Legendre polynomials with respect to a thickness coordinate.Thereby all equations of elasticity including Hooke’s law have been transformed to the corresponding equations for Fourier coefficients. Then in the same way as in the theory of elasticity, system of differential equations in term of displacements and boundary conditions for Fourier coefficients have been obtained. The Timoshenko’s and Euler-Bernoulli theories are based on the classical hypothesis and 2-D equations of linear micropolar elasticity in a special curvilinear system. The obtained equations can be used to calculate stress-strain and to model thin walled structures in macro, micro and nano scale when taking in to account micropolar couple stress and rotation effects.

Journal

Curved and Layered Structures – de Gruyter

Published: Jan 26, 2017

There are no references for this article.