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211.
Based on the first-order shear deformation plate theory with von Karman non-linearity, the non-linear axisymmetric and asymmetric behavior of functionally graded circular plates under transverse mechanical loading are investigated. Introducing a stress function and a potential function, the governing equations are uncoupled to form equations describing the interior and edge-zone problems of FG plates. This uncoupling is then used to conveniently present an analytical solution for the non-linear asymmetric deformation of an FG circular plate. A perturbation technique, in conjunction with Fourier series method to model the problem asymmetries, is used to obtain the solution for various clamped and simply supported boundary conditions. The material properties are graded through the plate thickness according to a power-law distribution of the volume fraction of the constituents. The results are verified by comparison with the existing results in the literature. The effects of non-linearity, material properties, boundary conditions, and boundary-layer phenomena on various response quantities in a solid circular plate are studied and discussed. It is found that linear analysis is inadequate for analysis of simply supported FG plates which are immovable in radial direction even in the small deflection range. Furthermore, the responses of FG materials under a positive load and a negative load of identical magnitude are not the same. It is observed that the boundary-layer width is approximately equal to the plate thickness with the boundary-layer effect in clamped FG plates being stronger than that in simply supported plates. 相似文献
212.
The problem of a penny-shaped interface crack between a functionally graded piezoelectric layer and a homogeneous piezoelectric
layer is investigated. The surfaces of the composite structure are subjected to both mechanical and electrical loads. The
crack surfaces are assumed to be electrically impermeable. Integral transform method is employed to reduce the problem to
a Fredholm integral equation of the second kind. The stress intensity factor, electric displacement intensity factor and energy
release rate are derived, some typical numerical results are plotted graphically. The effects of electrical loads, material
nonhomogeneity and crack configuration on the fracture behaviors of the cracked composite structure are analyzed in detail. 相似文献
213.
In this paper, an analytical solution is developed to determine deformations and stresses in circular disks made of functionally
graded materials subjected to internal and/or external pressure. Taking mechanical properties of the materials of circular
disks to be linear variations, the governing equation is derived from basic equations of axisymmetric, plane stress problems
in elasticity. By transforming the governing equation into a hypergeometric equation, an accurate analytical solution of deformations
and stresses in circular disks is obtained. The comparison with the numerical solution indicates that both approaches give
very agreeable results, indicating correctness of the proposed analytical solution. The obtained analytical solution is employed
to determine the radial displacement and stresses in circular disks subjected to external pressure, internal pressure, and
internal and external pressure, respectively. How the radius ratio of circular disks affects deformations and stresses is
also investigated. 相似文献
214.
Consider two bonded functionally graded piezoelectric material (FGPM) with finite height. Each material contains an arbitrary oriented crack. The material properties are assumed in exponential forms in the direction normal to the interface. The crack surface condition is assumed to be electrically impermeable or permeable. Using the Fourier transform technique, the problem can be reduced to a system of singular integral equations, which are then solved numerically by applying the Gauss-Chebyshev integration formula to obtain the stress intensity factors at the crack tips. Numerical calculations are carried out to obtain the energy density factor S and the energy release rate G. In impermeable case, the energy release rate has been shown to be negative as the electric loads are applied. The positive definite characteristic of the energy density factor makes it possible for predicting the fracture behavior of the cracked structure. The influences of the non-homogeneous parameters and crack orientation on the energy density factors at the crack tips are discussed in detail. The results show that the energy density factor at the crack tip will be increased when the crack tip is located within the softer material. 相似文献
215.
I.S. Choi A.J. Detor M. Dao S. Suresh 《Journal of the mechanics and physics of solids》2008,56(1):172-183
A systematic study of depth-sensing indentation was performed on nanocrystalline (nc) Ni-W alloys specially synthesized with controlled unidirectional gradients in plastic properties. A yield strength gradient and a roughly constant Young's modulus were achieved in the nc alloys, using electrodeposition techniques. The force vs. displacement response from instrumented indentation experiments matched very well with that predicted from the analysis of Part I of this paper. The experiments also revealed that the pile-up of the graded alloy around the indenter is noticeably higher than that for the two homogeneous reference alloys that constitute the bounding conditions for the graded material. These trends are also consistent with the predictions of the indentation analysis. 相似文献
216.
This paper deals with the antiplane magnetoelectroelastic problem of an internal crack normal to the edge of a functionally
graded piezoelectric/piezomagnetic half plane. The properties of the material such as elastic modulus, piezoelectric constant,
dielectric constant, piezomagnetic coefficient, magnetoelectric coefficient and magnetic permeability are assumed in exponential
forms and vary along the crack direction. Fourier transforms are used to reduce the impermeable and permeable crack problems
to a system of singular integral equations, which is solved numerically by using the Gauss-Chebyshev integration technique.
The stress, electric displacement and magnetic induction intensity factors at the crack tips are determined numerically. The
energy density theory is applied to study the effects of nonhomogeneous material parameter β, edge conditions, location of the crack and load ratios on the fracture behavior of the internal crack. 相似文献
217.
Mehdi Bayat M. Saleem B.B. Sahari A.M.S. Hamouda E. Mahdi 《Mechanics Research Communications》2008,35(5):283-309
Elastic solutions for axisymmetric rotating disks made of functionally graded material with variable thickness are presented. The material properties and disk thickness profile are assumed to be represented by two power-law distributions. In the case of hollow disk, based on the form of the power-law distribution for the mechanical properties of the constituent components and the thickness profile function, both analytical and semi-analytical solutions are given under free–free and fixed-free boundary conditions. For the solid disk, only semi-analytical solution is presented. The effects of the material grading index and the geometry of the disk on the stresses and displacements are investigated. It is found that a functionally graded rotating disk with parabolic or hyperbolic convergent thickness profile has smaller stresses and displacements compared with that of uniform thickness. It is seen that the maximum radial stress for the solid functionally graded disk with parabolic thickness profile is not at the centre like uniform thickness disk. Results of this paper suggest that a rotating functionally graded disk with parabolic concave or hyperbolic convergent thickness profile can be more efficient than the one with uniform thickness. 相似文献
218.
Holm Altenbach Victor A. Eremeyev 《Archive of Applied Mechanics (Ingenieur Archiv)》2008,78(10):775-794
The classical plate theory can be applied to thin plates made of classical materials like steel. The first theory allowing
the analysis of such plates was elaborated by Kirchhoff. But this approach was connected with various limitations (e.g., constant
material properties in the thickness direction). In addition, some mathematical inconsistencies like the order of the governing
equation and the number of boundary conditions exist. During the last century many suggestions for improvements of the classical
plate theory were made. The engineering direction of improvements was ruled by applications (e.g., the use of laminates or
sandwiches as the plate material), and so new hypotheses for the derivation of the governing equations were introduced. In
addition, some mathematical approaches like power series expansions or asymptotic integration techniques were applied. A conceptional
different direction is connected with the direct approach in the plate theory. This paper presents the extension of Zhilin’s
direct approach to plates made of functionally graded materials.
The second author was supported by DFG grant 436RUS17/21/07. 相似文献
219.
In the present paper, the analytical solution for a radially piezoelectric functionally graded rotating hollow shaft is presented.
The variation of material properties is assumed to follow a power law along the radial direction of the shaft. Two resulting
fully coupled differential equations in terms of the displacement and electric potential are solved directly. Numerical results
for different shaft geometries with different profiles of inhomogeneity are also graphically displayed. 相似文献
220.
In the present study, a novel exact closed-form procedure based on the third order shear deformation plate theory is developed to analyze in-plane and out-of-plane frequency responses of circular/annular functionally graded material (FGM) plates embedded in piezoelectric layers for both close/open circuit electrical boundary conditions. Introducing a new analytical method, five governing partial deferential equations of motion beside Maxwell electrostatic equation are solved via an exact closed-form method. The high accuracy and reliability of the present approach is confirmed by comparing some of the present data with their counterparts reported in the literature. Finally, the effect of material properties, power law index and boundary conditions on the free vibration of the smart FGM plate are studied and discussed in detail. 相似文献