• Structural Engineering and Mechanics
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• 제69권2호
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• pp.145-153
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• 2019

Modified couple stress formulation and first order shear deformation theory are used for magneto-electro-elastic bending analysis of three-layered curved size-dependent beam subjected to mechanical, magnetic and electrical loads. The governing equations are derived using a displacement field including radial and transverse displacements of middle surface and a rotation component. Size dependency is accounted based on modified couple stress theory by employing a small scale parameter. The numerical results are presented to study the influence of small scale parameter, initial electric and magnetic potentials and opening angle on the magneto-electro-elastic bending results of curved micro beam.

• Kyungpook Mathematical Journal
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• 제61권2호
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• pp.323-351
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• 2021

The present paper addresses magnetohydrodynamic pulsating flow and heat transfer of two immiscible, incompressible, and conducting couple stress fluids between two permeable beds. The flow between the permeable beds is assumed to be governed by Stokes' [28] couple stress fluid flow equations, whereas the dynamics of permeable beds is determined by Darcy's law. In this study, matching conditions were used at the fluid-fluid interface, whereas the B-J slip boundary condition was employed at the fluid-porous interface. The governing equations were solved analytically, and the expressions for velocity, temperature, mass flux, skin friction, and rate of heat transfer were obtained. The analytical expressions were numerically evaluated, and the results are presented through graphs and tables.

• Journal of applied mathematics & informatics
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• 제37권5_6호
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• pp.507-519
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• 2019

The ground for this paper is to examine the generalized Stokes' first and second issues for an incompressible couple pressure liquid under isothermal conditions. Exact solutions for each problem are acquired by using the Laplace transform (LT) with respect to the time variable t and the sine Fourier transform (FT) with respect to the y-variable. Further, a comparison is given of the obtained results and the results of Devakar and Lyengar [1] and by using the four inverse Laplace transform algorithms (Stehfest's, Tzou's, Talbot, Fourier series) in the space time domain utilizing a numerical methodology. Moreover, velocity profiles are plotted and considered for various occasions and distinctive estimations of couple stress parameters. At the end, the outcomes are exhibited by graphs and in tabular forms.

• 한국지역사회생활과학회지
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• 제19권4호
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• pp.547-558
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• 2008

The purpose of this study was to identify a couple's parental efficacy combination and, then, analyze parental role-sharing and parenting stress according to this combination type. The subjects were 307 couples who have a child in 1st or 2nd grade. The main results were as follows: First, fathers and mothers, as a group, did not differ in terms of parental efficacy. Secondly, some demographic variables related to parental efficacy. Thirdly, there are more couples who have similar levels of parental efficacy than those who have different levels of parental efficacy. Fourth, no significant difference in parental role-sharing was found among the 4 types of couple's parental efficacy. Fifth, mothers had low parental stress when both of the couple had high levels of parental efficacy while fathers perceived low parental stress if only he, himself, had a high level of parental efficacy.

• Advances in nano research
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• 제8권3호
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• pp.191-202
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• 2020

The article brings the study of nonlocal, surface and the couple stress together to apparent the frequency retaliation of FG nanobeams (Functionally graded). For the examination of frequency retaliation, the article considers the accurate spot of neutral axis. This article aims to enhance the coherence of proposed model to accurately encapsulate the significant effects of the nonlocal stress field, size effects together with material length scale parameters. These considered parameters are assimilated through what are referred to as modified couple stress as well as nonlocal elasticity theories, which encompasses the stiffness-hardening and softening influence on the nanobeams frequency characteristics. Power-law distribution is followed by the functional gradation of the material across the beam width in the considered structure of the article. Following the well-known Hamilton's principle, fundamental basic equations alongside their correlated boundary conditions are solved analytically. Validation of the study is also done with published result. Distinct parameters (such as surface energy, slenderness ratio, as nonlocal material length scale and power-law exponent) influence is depicted graphically following the boundary conditions on non-dimensional FG nanobeams frequency.

• Structural Engineering and Mechanics
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• 제53권1호
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• pp.105-130
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• 2015

In this paper, the classical continuum mechanics is adopted and modified to be consistent with the unique behavior of micro/nano solids. At first, some kinematical principles are discussed to illustrate the effect of the discrete nature of the microstructure of micro/nano solids. The fundamental equations and relations of the modified couple stress theory are derived to illustrate the microstructural effects on nanostructures. Moreover, the effect of the material surface energy is incorporated into the modified continuum theory. Due to the reduced coordination of the surface atoms a residual stress field, namely surface pretension, is generated in the bulk structure of the continuum. The essential kinematical and kinetically relations of nano-continuums are derived and discussed. These essential relations are used to derive a size-dependent model for Mindlin functionally graded (FG) nano-plates. An analytical solution is derived to show the feasibility of the proposed size-dependent model. A parametric study is provided to express the effect of surface parameters and the effect of the microstructure couple stress on the bending behavior of a simply supported FG nano plate.

• Coupled systems mechanics
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• 제9권6호
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• pp.521-538
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• 2020

The present study is concerned with the thermoelastic interactions in a two dimensional homogeneous, transversely isotropic thermoelastic solid with new modified couple stress theory without energy dissipation and with two temperatures in frequency domain. The time harmonic sources and Hankel transform technique have been employed to find the general solution to the field equations.Concentrated normal force, normal force over the circular region, thermal point source and thermal source over the circular region have been taken to illustrate the application of the approach. The components of displacements, stress, couple stress and conductive temperature distribution are obtained in the transformed domain. The resulting quantities are obtained in the physical domain by using numerical inversion technique. Numerically simulated results are depicted graphically to show the effect of angular frequency on the resulted quantities.

• Structural Engineering and Mechanics
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• 제64권4호
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• pp.403-411
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• 2017

In this article, analytical solution for free vibration of micro composite laminated beam on elastic medium based on modified couple stress are presented. The surrounding elastic medium is modeled as the Winkler elastic foundation. The governing equations and boundary conditions are obtained by using the principle of minimum potential energy for EulerBernoulli beam. For investigating the effect of different parameters including material length scale, beam thickness, some numerical results on different cross ply laminated beams such as (90,0,90), (0,90,0), (90,90,90) and (0,0,0) are presented on elastic medium. Free vibration analysis of a simply supported beam is considered utilizing the Fourier series. Also, the fundamental frequency is obtained using the principle of Hamilton for four types of cross ply laminations with hinged-hinged boundary conditions and different beam theories. The fundamental frequency for different thin beam theories are investigated by increasing the slenderness ratio and various foundation coefficients. The results prove that the modified couple stress theory increases the natural frequency under the various foundation for free vibration of composite laminated micro beams.

• Steel and Composite Structures
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• 제26권5호
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• pp.607-620
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• 2018

Vibration analysis of deep curved FG nano-beam has been carried out based on modified couple stress theory. Material properties of curved Timoshenko beam are assumed to be functionally graded in radial direction. Governing equations of motion and related boundary conditions have been obtained via Hamilton's principle. In a parametric study, influence of length scale parameter, aspect ratio, gradient index, opening angle, mode number and interactive influences of these parameters on natural frequency of the beam, have been investigated. It was found that, considering geometrical deepness term leads to an increase in sensitivity of natural frequency about variation of aforementioned parameters.

• Steel and Composite Structures
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• 제26권1호
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• pp.89-102
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• 2018

This work investigates a novel plate formulation and a modified couple stress theory that introduces a variable length scale parameter is presented to discuss the static and dynamic of functionally graded (FG) micro-plates. A new type of third-order shear deformation theory of Reddy that use only 4 unknowns by including undetermined integral variables is proposed in this study. The equations of motion are derived from Hamilton's principle. Analytical solutions are obtained for a simply supported micro-plate. Numerical examples are presented to examine the effect of the length scale parameter on the responses of micro-plates. The obtained results are compared with the previously published results to demonstrate the correctness of the present formulation.