• Steel and Composite Structures
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• 제22권1호
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• pp.91-112
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• 2016

In this paper, post-buckling behavior of sandwich plates with functionally graded (FG) face sheets under uniform temperature rise loading is examined based on both sinusoidal shear deformation theory and stress function. It is supposed that the sandwich plate is in contact with an elastic foundation during deformation, which acts in both compression and tension. Thermo-elastic non-homogeneous properties of FG layers change smoothly by the variation of power law within the thickness, and temperature dependency of material constituents is considered in the formulation. In the present development, Von Karman nonlinearity and initial geometrical imperfection of sandwich plate are also taken into account. By employing Galerkin method, analytical solutions of thermal buckling and post-buckling equilibrium paths for simply supported plates are determined. Numerical examples presented in the present study discuss the effects of gradient index, sandwich plate geometry, geometrical imperfection, temperature dependency, and the elastic foundation parameters.

• Steel and Composite Structures
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• 제26권6호
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• pp.663-672
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• 2018

This paper contains a consistent couple-stress theory to capture size effects in Euler-Bernoulli nano-beams made of three-directional functionally graded materials (TDFGMs). These models can degenerate into the classical models if the material length scale parameter is taken to be zero. In this theory, the couple-stress tensor is skew-symmetric and energy conjugate to the skew-symmetric part of the rotation gradients as the curvature tensor. The material properties except Poisson's ratio are assumed to be graded in all three axial, thickness and width directions, which it can vary according to an arbitrary function. The governing equations are obtained using the concept of minimum potential energy. Generalized differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the natural frequencies of TDFG nano-beam. At the end, some numerical results are performed to investigate some effective parameter on buckling load. In this theory the couple-stress tensor is skew-symmetric and energy conjugate to the skew-symmetric part of the rotation gradients as the curvature tensor.

• Structural Engineering and Mechanics
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• 제51권6호
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• pp.939-953
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• 2014

Using the infinitesimal theory of elasticity and analytical formulation based on the first-order shear deformation theory (FSDT) is presented for axisymmetric thick-walled cylinders made of functionally graded materials under internal and/or external uniform pressure. The material is assumed to be isotropic heterogeneous with constant Poisson's ratio and radially exponentially varying elastic modulus. At first, general governing equations of the FGM thick cylinders are derived by assumptions of the FSDT. Then the obtained equations are solved under the generalized clamped-clamped conditions. The results are compared with the findings of both FSDT and finite element method (FEM).

• Steel and Composite Structures
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• 제29권3호
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• pp.363-377
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• 2018

An efficient and free of shear locking finite element model is developed and employed to study free vibration of tapered bidirectional functionally graded material (BFGM) beams. The beam material is assumed to be formed from four distinct constituent materials whose volume fraction continuously varies along the longitudinal and thickness directions by power-law functions. The finite element formulation based on the first-order shear deformation theory is derived by using hierarchical functions to interpolate the displacement field. In order to improve efficiency and accuracy of the formulation, the shear strain is constrained to constant and the exact variation of the cross-sectional profile is employed to compute the element stiffness and mass matrices. A comprehensive parametric study is carried out to highlight the influence of the material distribution, the taper and aspect ratios as well as the boundary conditions on the vibration characteristics. Numerical investigation reveals that the proposed model is efficient, and it is capable to evaluate the natural frequencies of BFGM beams by using a small number of the elements. It is also shown that the effect of the taper ratio on the fundamental frequency of the BFGM beams is significantly influenced by the boundary conditions. The present results are of benefit to optimum design of tapered FGM beam structures.

• Steel and Composite Structures
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• 제35권1호
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• pp.61-76
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• 2020

In this paper, the dynamic behaviour of an inclined functionally graded material (FGM) beam with different boundary conditions under a moving mass is investigated based on the first-order shear deformation theory (FSDT). The material properties vary continuously along the beam thickness based on the power-law distribution. The system of motion equations is derived by using Hamilton's principle. The finite element method (FEM) is adopted to develop a general solution procedure. The moving mass is considered on the top surface of the beam instead of supposing it on the mid-plane. In order to consider the Coriolis, centrifugal accelerations and the friction force, the contact force method is used. Moreover, the effects of boundary conditions, the moving mass velocity and various material distributions are studied. For verification of the present results, a comparative fundamental frequency analysis of an FGM beam is conducted and the dynamic transverse displacements of the homogeneous and FGM beams traversed by a moving mass are compared with those in the existing literature. There is a good accord in all compared cases. In this study for the first time in dynamic analysis of the inclined FGM beams, the Coriolis and centrifugal accelerations of the moving mass are taken into account, and it is observed that these accelerations can be ignored for the low-speeds of the moving mass. The new provided results for dynamics of the inclined FGM beams traversed by a moving mass can be significant for the scientific and engineering community in the area of FGM structures.

• Advances in materials Research
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• 제5권4호
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• pp.245-261
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• 2016

Thermo-mechanical buckling problem of functionally graded (FG) nanoplates supported by Pasternak elastic foundation subjected to linearly/non-linearly varying loadings is analyzed via the nonlocal elasticity theory. Two opposite edges of the nanoplate are subjected to the linear and nonlinear varying normal stresses. Elastic properties of nanoplate change in spatial coordinate based on a power-law form. Eringen's nonlocal elasticity theory is exploited to describe the size dependency of nanoplate. The equations of motion for an embedded FG nanoplate are derived by using Hamilton principle and Eringen's nonlocal elasticity theory. Navier's method is presented to explore the influences of elastic foundation parameters, various thermal environments, small scale parameter, material composition and the plate geometrical parameters on buckling characteristics of the FG nanoplate. According to the numerical results, it is revealed that the proposed modeling can provide accurate results of the FG nanoplates as compared some cases in the literature. Numerical examples show that the buckling characteristics of the FG nanoplate are related to the material composition, temperature distribution, elastic foundation parameters, nonlocality effects and the different loading conditions.

• Advances in nano research
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• 제6권4호
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• pp.399-422
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• 2018

Unwanted vibration is an issue in many industrial systems, especially in nano-devices. There are many ways to compensate these unwanted vibrations based on the results of the past researches. Elastic medium and smart material etc. are effective methods to restrain unnecessary vibration. In this manuscript, dynamic analysis of viscoelastic nanosensor which is made of functionally graded (FGM) nanobeams is investigated. It is assumed that, the shaft is flexible. The system is modeled based on Timoshenko beam theory and also environmental condition, external linear varying loads and thermal loading effect are considered. The equations of motion are extracted by using energy method and Hamilton principle to describe the translational and shear deformation's behavior of the system. Governing equations of motion are extracted by supplementing Eringen's nonlocal theory. Finally vibration behavior of system especially the frequency of system is developed by implementation Semi-analytical differential transformed method (DTM). The results are validated in the researches that have been done in the past and shows good agreement with them.

• Advances in materials Research
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• 제12권2호
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• pp.161-177
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• 2023

This paper proposes an analytical method to investigate the free vibration behaviour of new functionally graded (FG) carbon nanotubes reinforced composite beams based on a higher-order shear deformation theory. Cosine functions represent the material gradation and material properties via the thickness. The kinematic relations of the beam are proposed according to trigonometric functions. The equilibrium equations are obtained using the virtual work principle and solved using Navier's method. A comparative evaluation of results against predictions from literature demonstrates the accuracy of the proposed analytical model. Moreover, a detailed parametric analysis checks for the sensitivity of the vibration response of FG nanobeams to nonlocal length scale, strain gradient microstructure-scale, material distribution and geometry.

• 한국재료학회:학술대회논문집
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• 한국재료학회 2008년도 춘계학술발표대회 및 제14회 신소재 심포지엄
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• pp.42.2-42.2
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• 2008

• Structural Engineering and Mechanics
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• 제53권5호
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• pp.981-995
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• 2015

This paper presents a finite element procedure for dynamic analysis of non-uniform Timoshenko beams made of axially Functionally Graded Material (FGM) under multiple moving point loads. The material properties are assumed to vary continuously in the longitudinal direction according to a predefined power law equation. A beam element, taking the effects of shear deformation and cross-sectional variation into account, is formulated by using exact polynomials derived from the governing differential equations of a uniform homogenous Timoshenko beam element. The dynamic responses of the beams are computed by using the implicit Newmark method. The numerical results show that the dynamic characteristics of the beams are greatly influenced by the number of moving point loads. The effects of the distance between the loads, material non-homogeneity, section profiles as well as aspect ratio on the dynamic responses of the beams are also investigated in detail and highlighted.