• International Journal of Aeronautical and Space Sciences
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• v.2 no.2
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• pp.46-55
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• 2001

A Green's function approach based on the laminate theory is adopted to obtain the unsteady temperature distributions in a semi-infinite hollow circular cylinder made of functionally graded materials (FGMs). The transient heat conduction equation based on the laminate theory is formulated into an eigenvalue problem for each layer by using the eigenfunction expansion theory and the separation of variables. The eigenvalues and the corresponding eigenfunctions obtained by solving an eigenvalue problem for each layer constitute the Green's function solution for analyzing the unsteady temperature distributions. Numerical calculations are carried out for the semi-infinite hollow circular FGM cylinder subjected to partially heated loads, and the numerical results are shown in figures.

• International Journal of Aerospace System Engineering
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• v.3 no.1
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• pp.1-4
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• 2016

Functionally graded materials (FGMs) are becoming very popular in various industries due to their effectiveness of the utilization of their constituent elements. However, the modelling of these materials is difficult due to the complex nature of variation of material properties across the thickness. Many shear deformation theories have been developed and employed for the analysis of such functionally graded plates (FGPs). A recently developed inverse hyperbolic shear deformation theory has been successfully employed by Grover et al. [1] for the analysis of laminated composites and sandwich plates. The objective of the study is to obtain finite element solution for the structural analysis of functionally graded plates using inverse hyperbolic shear deformation theory. Finite element analysis facilitates the analysis of complex problems such as functionally graded plates with different boundary conditions and different loadings.

• Structural Engineering and Mechanics
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• v.24 no.6
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• pp.727-740
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• 2006

A simple plane-strain solution is derived in this paper for the functionally graded multilayered isotropic elastic cylinder under static deformation. The solution is obtained using method of separation of variables and is expressed in terms of the summation of the Fourier series in the circumferential direction. While the solution for order n = 0 corresponds to the axisymmetric deformation, that for n = 2 includes the special deformation frequently utilized in the upper and lower bounds analysis. Numerical results for a three-phase cylinder with a middle functionally graded layer are presented for both axisymmetric (n = 0) and general (n = 2) deformations, under either the traction or displacement boundary conditions on the surface of the layered cylinder. The solution to the general deformation case (n = 2) is further utilized for the first time to find the upper and lower bounds of the effective shear modulus of the layered cylinder with a functionally graded middle layer. These results could be useful in the future study of cylindrical composites where FGMs and/or multilayers are involved.

• Geomechanics and Engineering
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• v.9 no.3
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• pp.361-372
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• 2015

In this paper, a refined exponential shear deformation theory for free vibration analysis of functionally graded beam with considering porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. For this purpose, a new displacement field based on refined shear deformation theory is implemented. The theory accounts for parabolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the beam without using shear correction factors. Based on the present refined shear deformation beam theory, the equations of motion are derived from Hamilton's principle. The rule of mixture is modified to describe and approximate material properties of the FG beams with porosity phases. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions. Illustrative examples are given also to show the effects of varying gradients, porosity volume fraction, aspect ratios, and thickness to length ratios on the free vibration of the FG beams.

• Structural Engineering and Mechanics
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• v.32 no.6
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• pp.811-833
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• 2009

In the present article bending, buckling and vibration analyses of tapered beams using Eringen non-local elasticity theory are being carried out. The associated governing differential equations are solved employing Rayleigh-Ritz method. Both Euler-Bernoulli and Timoshenko beam theories are considered in the analyses. Present results are in good agreement with those reported in literature. Beam material is considered to be made up of functionally graded materials (fgms). Non-local analyses for tapered beam with simply supported - simply supported, clamped - simply supported and clamped - free boundary conditions are carried out and discussed. Further, effect of length to height ratio on maximum deflections, vibration frequencies and critical buckling loads are studied.

• Advances in nano research
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• v.8 no.2
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• pp.149-156
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• 2020

The present paper explores forced vibrational properties of porosity-dependent functionally graded (FG) cylindrical nanoshells exposed to linear-type or triangular-type impulse load via classical shell theory (CST) and nonlocal strain gradient theory (NSGT). Employing such scale-dependent theory, two scale factors accounting for stiffness softening and hardening effects are incorporated in modeling of the nanoshell. Two sorts of porosity distributions called even and uneven have been taken into account. Governing equations obtained for porous nanoshell have been solved through inverse Laplace transforms technique to derive dynamical deflections. It is shown that transient responses of a nanoshell are affected by the form and position of impulse loading, amount of porosities, porosities dispensation, nonlocal and strain gradient factors.

• Proceedings of the KSME Conference
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• 2004.04a
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• pp.48-53
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• 2004

This paper suggested the method determing the stress intensity factor (SIF) for functionally gradient materials (FGMs) by photo elastic experimental method. The SIF for the center crack in a finite rectangulat plate with a linear variation of shear modulus with constant density and Poisson's ratio along the direction of the crack under mode I static loading is obtained. The exponential and linear variation of stress fields are used for obtaining the SIF. The greater crack length, the increaser the difference of the SIF between right and left side crack tip.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.25 no.6
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• pp.988-995
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• 2001

Functionally graded materials(FGMs) are highlighted to be suitable for high temperature engineering due to their continuous distribution of material properties. In this paper, an optimal design is executed for determining the optimal material volume distribution pattern that minimizes the steady-state thermal stress of FGM heat-resisting composites. The interior penalty function method and the golden section method are employed as optimization techniques while the finite element method is used for thermal stress analysis. Through numerical simulations we suggest the volume fraction distributions that considerably improve initial thermal stress distributions.

• Structural Engineering and Mechanics
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• v.57 no.5
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• pp.823-835
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• 2016

Using the Complementary Functions Method (CFM), a general solution for the one-dimensional steady-state thermal and mechanical stresses in a hollow thick sphere made of functionally graded material (FGM) is presented. The mechanical properties are assumed to obey the exponential variations in the radial direction, and the Poisson's ratio is assumed to be constant, with general thermal and mechanical boundary conditions on the inside and outside surfaces of the sphere. In the present paper, a semi-analytical iterative technique, one of the most efficient unified method, is employed to solve the heat conduction equation and the Navier equation. For different values of inhomogeneity constant, distributions of radial displacement, radial stress, circumferential stress, and effective stress, as a function of radial direction, are obtained. Various material models from the literature are used and corresponding temperature distributions and stress distributions are computed. Verification of the proposed method is done using benchmark solutions available in the literature for some special cases and virtually exact results are obtained.

• Coupled systems mechanics
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• v.2 no.3
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• pp.215-230
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• 2013

This paper investigates the pull-in instability of functionally graded poly-SiGe micro-beams under the combined electrostatic and intermolecular forces and temperature change. The exponential distribution model and Voigt model are used to analyze the functionally graded materials (FGMs). Principle of virtual work is used to derive the nonlinear governing differential equation which is then solved using differential quadrature method (DQM). A parametric study is conducted to show the significant effects of material composition, geometric nonlinearity, temperature change and intermolecular Casimir force.