scholarly journals The Fundamental Matrix of the System of Linear Micropolar Elasticity

2004 ◽  
pp. 825-831 ◽  
Author(s):  
Jerzy Gawinecki ◽  
Gerhard Kirchner ◽  
Jaroslaw Lazuka
Keyword(s):  
Fundamental Matrix ◽  
Micropolar Elasticity ◽  
Linear Micropolar Elasticity

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

2017 ◽  
Vol 4 (1) ◽  
pp. 104-118 ◽  
Author(s):  
V.V. Zozulya
Keyword(s):  
Fourier Series ◽  
Legendre Polynomials ◽  
Fourier Coefficients ◽  
Order Theory ◽  
Theory Of Elasticity ◽  
Micropolar Elasticity ◽  
Elasticity System ◽  
Thin Walled Structures ◽  
Curved Rods ◽  
Linear Micropolar Elasticity

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.

scholarly journals On Finite Element Computations of Contact Problems in Micropolar Elasticity

2016 ◽  
Vol 2016 ◽  
pp. 1-9 ◽  
Author(s):  
Victor A. Eremeyev ◽  
Andrzej Skrzat ◽  
Feliks Stachowicz
Keyword(s):  
Finite Element ◽  
Stress Concentration ◽  
Contact Area ◽  
Contact Problems ◽  
Micropolar Elasticity ◽  
Isoparametric Element ◽  
Classical Elasticity ◽  
Elastic Substrate ◽  
Commercial Software ◽  
Linear Micropolar Elasticity

Within the linear micropolar elasticity we discuss the development of new finite element and its implementation in commercial software. Here we implement the developed 8-node hybrid isoparametric element into ABAQUS and perform solutions of contact problems. We consider the contact of polymeric stamp modelled within the micropolar elasticity with an elastic substrate. The peculiarities of modelling of contact problems with a user defined finite element in ABAQUS are discussed. The provided comparison of solutions obtained within the micropolar and classical elasticity shows the influence of micropolar properties on stress concentration in the vicinity of contact area.

scholarly journals Representation of Waves of Displacements and Micro-rotations by Systems of the Screw Vector Fields

2020 ◽  
Vol 20 (4) ◽  
pp. 468-477
Author(s):  
Yuri N. Radayev ◽  
Keyword(s):  
Differential Equations ◽  
Linear Theory ◽  
Vector Fields ◽  
Harmonic Waves ◽  
Micropolar Elasticity ◽  
Cylindrical Waveguides ◽  
Physical Fields ◽  
Waves Propagation ◽  
Vector Differential Equation ◽  
Linear Micropolar Elasticity

The present study concerns the coupled vector differential equations of the linear theory of micropolar elasticity formulated in terms of displacements and micro-rotations in the case of a harmonic dependence of the physical fields on time. The system is known from many previous discussions on the micropolar elasticity. A new analysis aimed at uncoupling the coupled vector differential equation of the linear theory of micropolar elasticity is carried out. A notion of proportionality of the vortex parts of the displacements and microrotations to a single vector, which satisfies the screw equation, is employed. Finally the problem of finding the vortex parts of the displacements and micro-rotations fields is reduced to solution of four uncoupled screw differential equations. Corresponding representation formulae are given. Obtained results can be applied to problems of the linear micropolar elasticity concerning harmonic waves propagation along cylindrical waveguides.

Fundamental matrix of planar catadioptric stereo systems

2010 ◽  
Vol 4 (2) ◽  
pp. 85 ◽  
Author(s):  
H.-H.P. Wu ◽  
S.-H. Chang
Keyword(s):  
Fundamental Matrix
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