• Structural Monitoring and Maintenance
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• v.7 no.2
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• pp.69-84
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• 2020

Based on differential quadrature method (DQM) and nonlocal strain gradient theory (NSGT), forced vibrations of a porous functionally graded (FG) scale-dependent beam in thermal environments have been investigated in this study. The nanobeam is assumed to be in contact with a moving point load. NSGT contains nonlocal stress field impacts together with the microstructure-dependent strains gradient impacts. The nano-size beam is constructed by functionally graded materials (FGMs) containing even and un-even pore dispersions within the material texture. The gradual material characteristics based upon pore effects have been characterized using refined power-law functions. Dynamical deflections of the nano-size beam have been calculated using DQM and Laplace transform technique. The prominence of temperature rise, nonlocal factor, strain gradient factor, travelling load speed, pore factor/distribution and elastic substrate on forced vibrational behaviors of nano-size beams have been explored.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.20 no.7
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• pp.2134-2140
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• 1996

This study was carried out to anlayze the heat-resistant characteristics of functionally gradient material(FGM) composed with ceramic and metal. The thermal fracture behavior of plasma-sprayed FGM and conventional coating material(NFGM) was exaimined by acoustic emession technique under heating and cooling. Furnace cooling and rapid cooling tests were used to examine the effect of temperature change under various conditions, respectively. At the high temperature above $800^{\circ}C$, it was shown that FGM gives higher thermal resistance compared to NFGM by AE signal and fracture surface analysis.

• Structural Engineering and Mechanics
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• v.75 no.6
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• pp.659-674
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• 2020

The present paper employs nonlocal strain gradient theory (NSGT) to study buckling behavior of functionally graded magneto-electro-thermo-elastic (FG-METE) nanoshells under various physical fields. NSGT modeling of the nanoshell contains two size parameters, one related to nonlocal stress field and another related to strain gradients. It is considered that mechanical, thermal, electrical and magnetic loads are exerted to the nanoshell. Temperature field has uniform and linear variation in nanoshell thickness. According to a power-law function, piezo-magnetic, thermal and mechanical properties of the nanoshell are considered to be graded in thickness direction. Five coupled governing equations have been obtained by using Hamilton's principle and then solved implementing Galerkin's method. Influences of temperature field, electric voltage, magnetic potential, nonlocality, strain gradient parameter and FG material exponent on buckling loads of the FG-METE nanoshell have been studied in detail.

• Steel and Composite Structures
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• v.42 no.5
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• pp.599-615
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• 2022

In the present paper, the numerical dynamic analysis of a functionally graded nano-scale nonuniform tube was investigated according to the high-order beam theory coupled with the nonlocal gradient strain theory. The supposed cross-section is changed along the pipe length, and the material distribution, which combines both metal and ceramics, is smoothly changed in the pipe length direction, which is called axially functionally graded (AFG) pipe. Moreover, the porosity voids are dispersed in the cross-section and the radial pattern that the existence of both material distribution along the tube length and porosity voids make a two-dimensional functionally graded (2D-FG) truncated conical pipe. On the basis of the Hamilton principle, the governing equations and the associated boundary conditions equations are derived, and then a numerical approach is applied to solve the obtained equations.

• Structural Engineering and Mechanics
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• v.20 no.4
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• pp.435-450
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• 2005

Here, the dynamic instability characteristics of aero-thermo-mechanically stressed functionally graded plates are investigated using finite element procedure. Temperature field is assumed to be a uniform distribution over the plate surface and varied in thickness direction only. Material properties are assumed to be temperature dependent and graded in the thickness direction according to simple power law distribution. For the numerical illustrations, silicon nitride/stainless steel is considered as functionally graded material. The aerodynamic pressure is evaluated based on first-order high Mach number approximation to the linear potential flow theory. The boundaries of the instability region are obtained using the principle of Bolotin's method and are conveniently represented in the non-dimensional excitation frequency-load amplitude plane. The variation dynamic instability width is highlighted considering various parameters such as gradient index, temperature, aerodynamic and mechanical loads, thickness and aspect ratios, and boundary condition.

• Composites Research
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• v.16 no.5
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• pp.21-27
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• 2003

Using the theory of linear piezoelectricity, the dynamic response of a central crack in a functionally graded piezoelectric ceramic under anti-plane shear impact is analyzed. We assume that the properties of the functionally graded piezoelectric material vary continuously along the thickness. By using the Laplace and Fourier transform, the problem is reduced to two pairs of dual integral equations and then into Fredholm integral equations of the second kind. Numerical values on the dynamic stress intensity factors are presented to show the dependence of the gradient of material properties and electric loading.

• Steel and Composite Structures
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• v.23 no.3
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• pp.263-271
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• 2017

A theoretical study was carried-out of mode II delamination fracture behavior of the End Loaded Split (ELS) functionally graded beam configuration with considering the material non-linearity. The mechanical response of ELS was modeled analytically by using a power-law stress-strain relation. It was assumed that the material is functionally graded transversally to the beam. The non-linear fracture was investigated by using the J-integral approach. Equations were derived for the crack arm curvature and zero axes coordinate that are needed for the J-integral solution. The analysis developed is valid for a delamination crack located arbitrary along the beam height. The J-integral solution was verified by analyzing the strain energy release rate with considering material non-linearity. The effects of material gradient, non-linear material behavior and crack location on the fracture were evaluated. The solution derived is suitable for parametric analyses of non-linear fracture. The results obtained can be used for optimization of functionally graded beams with respect to their mode II fracture performance. Also, such simplified analytical models contribute for the understanding of delamination fracture in functionally graded beams exhibiting material non-linearity.

• Structural Engineering and Mechanics
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• v.69 no.2
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• pp.205-219
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• 2019

This paper analyzes nonlinear free vibration of the circular nano-tubes made of functionally graded materials in the framework of nonlocal strain gradient theory in conjunction with a refined higher order shear deformation beam model. The effective material properties of the tube related to the change of temperature are assumed to vary along the radius of tube based on the power law. The refined beam model is introduced which not only contains transverse shear deformation but also satisfies the stress boundary conditions where shear stress cancels each other out on the inner and outer surfaces. Moreover, it can degenerate the Euler beam model, the Timoshenko beam model and the Reddy beam model. By incorporating this model with Hamilton's principle, the nonlinear vibration equations are established. The equations, including a material length scale parameter as well as a nonlocal parameter, can describe the size-dependent in linear and nonlinear vibration of FGM nanotubes. Analytical solution is obtained by using a two-steps perturbation method. Several comparisons are performed to validate the present analysis. Eventually, the effects of various physical parameters on nonlinear and linear natural frequencies of FGM nanotubes are analyzed, such as inner radius, temperature, nonlocal parameter, strain gradient parameter, scale parameter ratio, slenderness ratio, volume indexes, different beam models.

• Computers and Concrete
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• v.30 no.2
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• pp.151-164
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• 2022

This paper investigates the stability of the functionally graded cylindrical small-scale tube regarding the dynamic analysis and based on the modified nonclassical high-order nonlocal strain gradient theory. The nonlocal beam is modeled according to the high-order tube theory utilizing the energy method based on the Hamilton principle, then the nonlocal governing equations and also nonlocal boundary conditions equations are obtained. The tube structure is made of the new class of composite material composed of ceramic and metal phases as the functionally graded structures. The functionally graded (FG) tube structures rotate around the central axis, and the stability of this nanodevice is due to the centrifugal force which is used for the application of nanoelectromechanical systems (NEMS) is studied in detail.

• Coupled systems mechanics
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• v.7 no.4
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• pp.441-453
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• 2018

Longitudinal fracture in a functionally graded beam configuration was studied analytically with taking into account the non-linear behavior of the material. A cantilever beam with two longitudinal cracks located symmetrically with respect to the centroid was analyzed. The material was functionally graded along the beam width as well as along the beam length. The fracture was studied in terms of the strain energy release rate. The influence of material gradient, crack location along the beam width, crack length and material non-linearity on the fracture behavior was investigated. It was shown that the analytical solution derived is very useful for parametric analyses of the non-linear longitudinal fracture behavior. It was found that by using appropriate material gradients in width and length directions of the beam, the strain energy release rate can be reduced significantly. Thus, the results obtained in the present paper may be applied for optimization of functionally graded beam structure with respect to the longitudinal fracture performance.