• Structural Engineering and Mechanics
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• v.65 no.1
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• pp.33-41
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• 2018

In this paper, using modified couple stress theory in place of classical continuum theory, and using shell model in place of beam model, vibrational behavior of nanotubes is investigated via the finite element method. Accordingly classical continuum theory is unable to correctly compute stiffness and account for size effects in micro/nanostructures, higher order continuum theories such as modified couple stress theory have taken on great appeal. In the present work the mass-stiffness matrix for cylindrical shell element is developed, and by means of size-dependent finite element formulation is extended to more precisely account for nanotube vibration. In addition to modified couple stress cylindrical shell element, the classical cylindrical shell element can also be defined by setting length scale parameter to zero in the equations. The boundary condition were assumed simply supported at both ends and it is shown that the natural frequency of nano-scale shell using the modified coupled stress theory is larger than that using the classical shell theory and the results of Ansys. The results have indicated using the modified couple stress cylindrical shell element, the rigidity of the nano-shell is greater than that in the classical continuum theory, which results in increase in natural frequencies. Besides, in addition to reducing the number of elements required, the use of this type of element also increases convergence speed and accuracy.

• Steel and Composite Structures
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• v.45 no.6
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• pp.851-863
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• 2022

This research deals with the study of the Thomson heating effect in magneto-thermoelastic homogeneous isotropic rotating medium, influenced by linearly distributed load and as a result of modified couple stress theory. The charge density is taken as a function of the time of the induced electric current. The heat conduction equation with energy dissipation and with hyperbolic two-temperature (H2T) is used to formulate the model of the problem. Laplace and Fourier transforms are used to solve this mathematical model. Various components of displacement, temperature change, and axial stress as well as couple stress are obtained from the transformed domain. To get the solution in physical domain, numerical inversion techniques have been employed. The Thomson effect with GN (Green-Nagdhi) -III theory and Modified Couple Stress Theory (MCST) is shown graphically on the physical quantities.

• Geomechanics and Engineering
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• v.19 no.5
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• pp.369-381
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• 2019

The objective of this paper is to study the two dimensional deformation in transversely isotropic thermoelastic medium without energy dissipation due to time harmonic sources using new modified couple stress theory, a continuum theory capable to predict the size effects at micro/nano scale. The couple stress constitutive relationships have been introduced for transversely isotropic thermoelastic medium, in which the curvature tensor is asymmetric and the couple stress moment tensor is symmetric. Fourier transform technique is applied to obtain the solutions of the governing equations. Assuming the deformation to be harmonically time-dependent, the transformed solution is obtained in the frequency domain. The application of a time harmonic concentrated and distributed sources have been considered to show the utility of the solution obtained. The displacement components, stress components, temperature change and couple stress are obtained in the transformed domain. A numerical inversion technique has been used to obtain the solutions in the physical domain. The effects of angular frequency are depicted graphically on the resulted quantities.

• Structural Engineering and Mechanics
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• v.76 no.1
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• pp.17-26
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• 2020

The objective of this paper is to study the deformation in transversely isotropic thermoelastic solid using new modified couple stress theory subjected to ramp-type thermal source and without energy dissipation. This theory contains three material length scale parameters which can determine the size effects. The couple stress constitutive relationships are introduced for transversely isotropic thermoelastic solid, in which the curvature (rotation gradient) tensor is asymmetric and the couple stress moment tensor is symmetric. Laplace and Fourier transform technique is applied to obtain the solutions of the governing equations. The displacement components, stress components, temperature change and couple stress are obtained in the transformed domain. A numerical inversion technique has been used to obtain the solutions in the physical domain. The effects of length scale parameters are depicted graphically on the resulted quantities. Numerical results show that the proposed model can capture the scale effects of microstructures.

• Structural Engineering and Mechanics
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• v.46 no.3
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• pp.417-431
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• 2013

This paper presents responses of the free end of a cantilever micro beam under the effect of an impact force based on the modified couple stress theory. The beam is excited by a transverse triangular force impulse modulated by a harmonic motion. The Kelvin-Voigt model for the material of the beam is used. The considered problem is investigated within the Bernoulli-Euler beam theory by using energy based finite element method. The system of equations of motion is derived by using Lagrange's equations. The obtained system of linear differential equations is reduced to a linear algebraic equation system and solved in the time domain by using Newmark average acceleration method. In the study, the difference of the modified couple stress theory and the classical beam theory is investigated for the wave propagation. A few of the obtained results are compared with the previously published results. The influences of the material length scale parameter on the wave propagation are investigated in detail. It is clearly seen from the results that the classical beam theory based on the modified couple stress theory must be used instead of the classical theory for small values of beam height.

• Steel and Composite Structures
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• v.51 no.2
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• pp.103-116
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• 2024

Based on the consistent couple stress theory (CCST), we develop a unified formulation for analyzing the static bending and free vibration behaviors of functionally graded (FG) microscale beams (MBs). The strong forms of the CCST-based Euler-Bernoulli, Timoshenko, and Reddy beam theories, as well as the CCST-based sinusoidal, exponential, and hyperbolic shear deformation beam theories, can be obtained by assigning some specific shape functions of the shear deformations varying through the thickness direction of the FGMBs in the unified formulation. The above theories are thus included as special cases of the unified CCST. A comparative study between the results obtained using a variety of CCST-based beam theories and those obtained using their modified couple stress theory-based counterparts is carried out. The impacts of some essential factors on the deformation, stress, and natural frequency parameters of the FGMBs are examined, including the material length-scale parameter, the aspect ratio, and the material-property gradient index.

• Computers and Concrete
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• v.19 no.6
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• pp.701-710
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• 2017

In this study, the thermoelastic beam in modified couple stress theory due to laser source and heat flux is investigated. The beam are heated by a non-Guassian laser pulse and heat flux. The Euler Bernoulli beam theory and the Laplace transform technique are applied to solve the basic equations for coupled thermoelasticity. The simply-supported and isothermal boundary conditions are assumed for both ends of the beam. A general algorithm of the inverse Laplace transform is developed. The analytical results have been numerically analyzed with the help of MATLAB software. The numerically computed results for lateral deflection, thermal moment and axial stress due to laser source and heat flux have been presented graphically. Some comparisons have been shown in figures to estimate the effects of couple stress on the physical quantities. A particular case of interest is also derived. The study of laser-pulse find many applications in the field of biomedical, imaging processing, material processing and medicine with regard to diagnostics and therapy.

• Steel and Composite Structures
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• v.22 no.6
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• pp.1239-1259
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• 2016

The modified couple stress-based third-order shear deformation theory is presented for sigmoid functionally graded materials (S-FGM) plates. The advantage of the modified couple stress theory is the involvement of only one material length scale parameter which causes to create symmetric couple stress tensor and to use it more easily. Analytical solution for dynamic instability analysis of S-FGM plates on elastic medium is investigated. The present models contain two-constituent material variation through the plate thickness. The equations of motion are derived from Hamilton's energy principle. The governing equations are then written in the form of Mathieu-Hill equations and then Bolotin's method is employed to determine the instability regions. The boundaries of the instability regions are represented in the dynamic load and excitation frequency plane. It is assumed that the elastic medium is modeled as Pasternak elastic medium. The effects of static and dynamic load, power law index, material length scale parameter, side-to-thickness ratio, and elastic medium parameter have been discussed. The width of the instability region for an S-FGM plate decreases with the decrease of material length scale parameter. The study is relevant to the dynamic simulation of micro structures embedded in elastic medium subjected to intense compression and tension.

• Coupled systems mechanics
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• v.8 no.6
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• pp.501-522
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• 2019

The present study is concerned with the thermoelastic interactions in a two dimensional axisymmetric problem in transversely isotropic thermoelastic solid using new modified couple stress theory without energy dissipation and with two temperatures. The Laplace and Hankel transforms have been employed to find the general solution to the field equations. Concentrated normal force, normal force over the circular region, concentrated thermal 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. The effect of two temperature varying by taking different values for the two temperature on the components of normal stress, tangential stress, conductive temperature and couple stress are depicted graphically.

• Structural Engineering and Mechanics
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• v.69 no.2
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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.