scholarly journals Unilateral Contact of Elastic Bodies (Moment Theory)

2001 ◽  
Vol 8 (4) ◽  
pp. 753-766
Author(s):  
R. Gachechiladze
Keyword(s):  
Contact Zone ◽  
Couple Stress Theory ◽  
Contact Problems ◽  
Theory Of Elasticity ◽  
Unilateral Contact ◽  
Stress Theory ◽  
Nonhomogeneous Media ◽  
Elastic Bodies ◽  
The Moment ◽  
Boundary Contact

Abstract Boundary contact problems of statics of the moment (couple-stress) theory of elasticity are studied in the case of a unilateral contact of two elastic anisotropic nonhomogeneous media. A problem, in which during deformation the contact zone lies within the boundaries of some domain, and a problem, in which the contact zone can extend, are given a separate treatment. Concrete problems suitable for numerical realizations are considered.

Effect of Couple-Stresses on Force Transfer Between Embedded Microfibers

1967 ◽  
Vol 1 (2) ◽  
pp. 174-187 ◽  
Author(s):  
M.A. Sadowsky ◽  
Y.C. Hsu ◽  
M.A. Hussain
Keyword(s):  
Stress Field ◽  
Couple Stress Theory ◽  
Physical Phenomenon ◽  
Lattice Parameter ◽  
Theory Of Elasticity ◽  
Crystal Lattice Parameter ◽  
Tangential Displacement ◽  
Stress Theory ◽  
Couple Stresses ◽  
Force Transfer

The present investigation is a continuation of the Weitsman problem, reference 1. The investigation is concerned with the nature of the stress field which develops in the presence of couple- stresses in composite material formed of microfibers embedded in a filler substance. The case is considered when one row consists of an infinitely long microfiber, while the second row is composed of two semi- infinite microfibers. An exact solution, based on a two-dimensional theory of elastic ity with inclusion of couple-stresses is obtained for the stress field which is activated by giving the two semi-infinite microfibers a tangential displacement of separation. The couple-stress theory gives a better representation of the actual physical phenomenon than the classical theory of elasticity. This is especially true and essentially important for bodies having a dimension comparable to the crystal lattice parameter of the material. This is believed to be the case with an elastic microfilm in bond with microfibers. The investigation led to results which are at wide variance with the Weitsman solution near x = 0 and the asymptotic solution shows the same trend as reported previously in reference num bered 2 i.e., bonding layers are dominated by boundary layer behavior throughout their entire thickness.

scholarly journals Couple stress theory of curved rods. 2-D, high order, Timoshenko’s and Euler-Bernoulli models

2017 ◽  
Vol 4 (1) ◽  
pp. 119-133 ◽  
Author(s):  
V.V. Zozulya
Keyword(s):  
Fourier Series ◽  
Couple Stress ◽  
Legendre Polynomials ◽  
Fourier Coefficients ◽  
Couple Stress Theory ◽  
Order Theory ◽  
Theory Of Elasticity ◽  
High Order ◽  
Stress Theory ◽  
Curved Rods

AbstractNew models for plane curved rods based on linear couple stress theory of elasticity have been developed.2-D theory is developed from general 2-D equations of linear couple stress elasticity using a special curvilinear system of coordinates related to the middle line of the rod as well as 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 along with body forces have 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, a system of differential equations in terms of displacements and boundary conditions for Fourier coefficients have been obtained. Timoshenko’s and Euler-Bernoulli theories are based on the classical hypothesis and the 2-D equations of linear couple stress theory of 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 scales when taking into account couple stress and rotation effects.

Effects of the Length Scale Parameter on the Thermoelastic Damping of a Microbeam Considering the Couple Stress Theory

2016 ◽  
Vol 08 (06) ◽  
pp. 1650083 ◽  
Author(s):  
Mohammad Fathalilou ◽  
Ghader Rezazadeh
Keyword(s):  
Couple Stress ◽  
Scale Parameter ◽  
Couple Stress Theory ◽  
Theory Of Elasticity ◽  
Length Scale Parameter ◽  
Length Scale ◽  
Complex Frequency ◽  
Thermoelastic Damping ◽  
Stress Theory ◽  
Ambient Temperatures

This paper studies the thermoelastic damping in microbeams considering the couple stress theory with microstructure. This theory includes the microinertia effects, coming from the kinetic energy due to the velocity gradient through the differential macroelements. A Galerkin-based reduced order model and complex frequency approach have been used to determine the quality factor. For a gold microbeam as a case study, the obtained results for different ambient temperatures, beam lengths and thicknesses are compared to those obtained using the classic theory of elasticity. The comparison has been made for different values of the length scale parameter. The effects of the microinertia term on the magnitude of the thermoelastic damping have also been investigated and shown that for which conditions these effects are significant.

Potential methods in the linear couple-stress theory of elasticity

1972 ◽  
Vol 15 (3-4) ◽  
pp. 165-176 ◽  
Author(s):  
R. S. Dhaliwal ◽  
K. L. Chowdhury
Keyword(s):  
Couple Stress ◽  
Couple Stress Theory ◽  
Theory Of Elasticity ◽  
Stress Theory ◽  
Potential Methods
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