Showing 4 results for Functionally Graded Material
M. H. Yas, M. Nejati, S. S. Jafari,
Volume 35, Issue 2 (2-2017)
Abstract
In this paper, free vibration of carbon nanotube-reinforced functionally graded circular plates with hole has been
investigated. Distribution of carbon nanotubes are continuous and the gradual and graded changes of materials through the
plate thickness are considered as volume fraction. Considering the linear and non-linear variation of circular plates through the
radial direction and also considering the proposed function for the thickness, the plate thickness can be convex or concave.
Moreover, the motion equations of plate were obtained based on the third-order shear deformation theory. These equations are
coupled differential equations which can convert Ordinary Differential Equations (ODE) using the Trigonometric series
expansion of displacement fields such that they satisfy the axial symmetry condition. Solving the converted ODE equations is too
difficult. For this reason, the differential quadrature method is employed to solve these equations. The obtained results are
compared with the results reported by other researchers and an excellent agreement is observed between them. Finally, the effects
of different geometric parameters as well as different volume fracture of nanotubes on natural frequency have been studied.
N. Cheraghi, M. Miri, M. Rashki,
Volume 39, Issue 1 (8-2020)
Abstract
This paper presents a probabilistic assessment on the free vibration analysis of functionally graded material plates, including layers with magneto-electro-elastic properties, using the 3D solution and surrogate models. The plate is located on an elastic foundation and the intra-layer slipping effect is also considered in the analysis by employing the generalized intra-layer spring model. Due to the high computational cost of the 3D solution in calculating the free vibration frequency of the plate, surrogate models are used. The meta models including kriging method, radial fundamental function method and polynomial response surface method are used to construct the surrogate model. For surrogate models training, the results of the three-dimensional solving method are used. The elastic foundation hardness, the intra-layer slipping effect, the material properties index, and the layer densities are considered as the variables with uncertainty. The three-dimensional solution method is validated through a comparison with other available reference. The results obtained through the surrogate models have been compared to those of the 3D solution formulation, showing a good agreement. The effects of some parameters including the elastic foundation hardness, the intra-layer slipping effect, the density of each layer, and the material properties index on the fundamental frequency of functionally graded material plates are investigated. By using three-dimensional solution method and Kriging Surrogate Model, it is shown that the shear and transverse components of elastic foundation hardness and the density of each layer have the greatest effect on the fundamental frequency of the functionally graded material plates.
M. Hashemian, M. Jabbarzadeh,
Volume 40, Issue 1 (9-2021)
Abstract
In this paper, nonlinear bending analysis of functionally graded rectangular and sectorial micro/nano plates is investigated using the modified couple stress theory. For this purpose, a higher-order shear deformation theory and von Kármán geometrically nonlinear theory are employed. The equilibrium equations and the boundary conditions for rectangular and annular sector plates are derived from the principle of minimum total potential energy and solved using the Semi-Analytical Polynomial Method (SAPM). One of the advantages of the implemented shear deformation theory is removing the defects of higher order shear deformation theory, and obtaining the response of the first and the third-order shear deformation theories at the same time. Afterwards, beside investigating the benefits of this theory compared with other ones, the results are verified with those by other researches. At the end, the effects of length scale parameter, boundary conditions, power law index, and geometrical dimensions are investigated
M. Mohieddin Ghomshei, Sh. Namazi,
Volume 41, Issue 1 (9-2022)
Abstract
In this article, mechanical buckling analysis of tapered beams having constant width and variable thickness, made of two-dimensional functionally graded materials is studied. The beam is assumed to be made of metal and ceramic, where their volume fractions vary in both longitudinal and thickness directions based on the power law. The beam is generally subjected to combined concentrated and distributed axial loads. The set of governing equations are derived using the Principle of Minimum total Potential Energy (PMPE), and are solved numerically using Differential Quadrature Method (DQM) for clamped-free boundary conditions. Convergence and accuracy of the presented solution are confirmed for both cases of concentrated and distributed axial loads. The effects of different parameters on the critical buckling load of the beam for both load cases are studied including geometrical parameters, gradation indices in longitudinal and thickness directions, and variation of thickness. Also buckling analysis of the beam under a combination of concentrated load and distributed axial loads of linear, quadratic and exponential types are investigated. Numerical results show that the highest values of the critical buckling load belong to the linear distributed load, and the lowest value is owned by exponential load.
