فهرس المقالات Navier solution

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  1 - Vibration Analysis of Rectangular Kirchhoff Nano-Plate using Modified Couple Stress Theory and Navier Solution Method
  Behzad Bayati Chaleshtori Ali Hajiahmad Seyed Saeid Mohtasebi
  10.30495/admt.2021.1916102.1230
  In this study, the characteristics of rectangular Kirchhoff nano-plate vibrations are investigated using a modified couple stress theory. To consider the effects of small-scale, the modified couple stress theory proposed by Young (2002) is used as it has only one length أکثر

  In this study, the characteristics of rectangular Kirchhoff nano-plate vibrations are investigated using a modified couple stress theory. To consider the effects of small-scale, the modified couple stress theory proposed by Young (2002) is used as it has only one length scale parameter. In modified couple stress theory, the strain energy density is a function of the components of the strain tensor, curvature tensor, stress tensor, and symmetric part of the couple stress tensor. After obtaining the strain energy, external work, and kinetic energy equation and inserting them in the Hamilton principle, the main and auxiliary equations of nano-plate are obtained. Then, by applying the boundary and force conditions in the governing equations, the vibrations of the rectangular Kirschhof nano-plate with the thickness are investigated with simple support around. The solution method used in this study is the Navier method and the effects of material length scale, length and thickness of the nanoplate on the vibration are investigated and the results are presented and discussed in details. تفاصيل المقالة
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  2 - Analytical Solutions of the FG Thick Plates with In-Plane Stiffness Variation and Porous Substances Using Higher Order Shear Deformation Theory
  M karimi darani A Ghasemi
  This paper presents the governing equations on the rectangular plate with the variation of material stiffness through their thick using higher order shear deformation theory (HSDT). The governing equations are obtained by using Hamilton's principle with regard to variat أکثر

  This paper presents the governing equations on the rectangular plate with the variation of material stiffness through their thick using higher order shear deformation theory (HSDT). The governing equations are obtained by using Hamilton's principle with regard to variation of Young's modulus in through their thick with regard sinusoidal variation of the displacement field across the thickness. In addition, the effects of the substances in FG-porous plate are investigated. تفاصيل المقالة
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  3 - Assessment of Third‌-order Shear Deformation Graphene Nanoplate Response under Static Loading Using Modified Couple Stress Theory
  Majid Eskandari Shahraki Mahmoud Shariati Naser Asiaban Ali Davar Mohsen Heydari Beni Jafar Eskandari Jam
  In this paper bending and buckling characteristics of third-order shear, and deformation nanoplates were investigated using the modified couple stress theory and Navier type solution. It can be useful for designing and manufacturing micro-electromechanical and nano-elec أکثر

  In this paper bending and buckling characteristics of third-order shear, and deformation nanoplates were investigated using the modified couple stress theory and Navier type solution. It can be useful for designing and manufacturing micro-electromechanical and nano-electromechanical systems. The modified couple stress theory was applied to provide the possibility of considering the effects of small scales that have only one material length scale parameter. In this theory, the strain energy density is a function of the strain tensor components, curvature tensor, stress tensor, and the symmetric part of the couple stress tensor. After obtaining the strain energy, external work, and buckling equations, the Hamilton principle is employed to derive the governing equations. Furthermore, by applying boundary and loading conditions in the governing equations, the bending and buckling of a third-order shear deformation nanoplate with simply-supported bearings are obtained and the Navier’s solution is used to solve the equations. The results indicate that the third-order nanoplate subjected to sinusoidal loading yields smaller values of dimensionless bending than it does while subjected to uniform surface traction. It was also found that by increasing the length to thickness ratio, the value of the dimensionless bending of nanoplate decreases but by increasing the aspect ratio of the plate, this value increases. Furthermore, it was shown that the critical buckling load of the third-order nanoplate under uniaxial loading increases by increasing the ratio of the length scale parameter to the thickness of the nanoplate but it decreases by increasing the length to thickness ratio of the nanoplate. تفاصيل المقالة