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

Curved and Layered Structures (2017)

- Volume: 4, Issue: 1, page 104-118
- ISSN: 2353-7396

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topV.V. Zozulya. "Micropolar curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models." Curved and Layered Structures 4.1 (2017): 104-118. <http://eudml.org/doc/288536>.

@article{V2017,

abstract = {New 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.},

author = {V.V. Zozulya},

journal = {Curved and Layered Structures},

keywords = {Curved rod; micropolar; Legendre polynomial;Timoshenko theory; Euler-Bernoulli theory},

language = {eng},

number = {1},

pages = {104-118},

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

url = {http://eudml.org/doc/288536},

volume = {4},

year = {2017},

}

TY - JOUR

AU - V.V. Zozulya

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

JO - Curved and Layered Structures

PY - 2017

VL - 4

IS - 1

SP - 104

EP - 118

AB - New 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.

LA - eng

KW - Curved rod; micropolar; Legendre polynomial;Timoshenko theory; Euler-Bernoulli theory

UR - http://eudml.org/doc/288536

ER -