Stress analysis of a functional graded material plate with a circular hole

Yang, Qingchun; Gao, Cun‐Fa; Chen, Wentao

doi:10.1007/s00419-009-0349-3

Cited by 76 publications

(19 citation statements)

References 26 publications

(27 reference statements)

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“…113.463 (3) 91.928 (2) 91.928 (2) 77.619 (2) 38.688 (2) 38.688 (2) 34.955 (1) 34.955 (1) 22.309 (1) The superscript numbers within the parenthesis indicate the mode of buckling…”

Section: Effect Of Foundation Stiffness Coefficients On Critical Buckmentioning

confidence: 99%

“…(22) and the quadratic function form of in-plane loading into the stability Eq. (21) and applying the kinematic and constitutive relations, leads to the buckling equation as…”

Section: In-plane Loading Configurationmentioning

confidence: 99%

“…Jomehzadeh et al [21] developed an analytical solution for bending of moderately thick FG sector plates in polar coordinates using the boundary layer function. Yang et al [22] studied two-dimensional stress distribution of a functionally graded plate with a circular hole under arbitrary constant loads. Axisymmetric bending and buckling of functionally graded circular plates were investigated by Saidi et al [23] based on the unconstrained third-order shear deformation plate theory.…”

Section: Introductionmentioning

confidence: 99%

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Stability analysis of functionally graded rectangular plates under nonlinearly varying in-plane loading resting on elastic foundation

Bodaghi

Saidi

2010

Arch Appl Mech

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In this research work, an exact analytical solution for buckling of functionally graded rectangular plates subjected to non-uniformly distributed in-plane loading acting on two opposite simply supported edges is developed. It is assumed that the plate rests on two-parameter elastic foundation and its material properties vary through the thickness of the plate as a power function. The neutral surface position for such plate is determined, and the classical plate theory based on exact neutral surface position is employed to derive the governing stability equations. Considering Levy-type solution, the buckling equation reduces to an ordinary differential equation with variable coefficients. An exact analytical solution is obtained for this equation in the form of power series using the method of Frobenius. By considering sufficient terms in power series, the critical buckling load of functionally graded plate with different boundary conditions is determined. The accuracy of presented results is verified by appropriate convergence study, and the results are checked with those available in related literature. Furthermore, the effects of power of functionally graded material, aspect ratio, foundation stiffness coefficients and in-plane loading configuration together with different combinations of boundary conditions on the critical buckling load of functionally graded rectangular thin plate are studied.

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“…113.463 (3) 91.928 (2) 91.928 (2) 77.619 (2) 38.688 (2) 38.688 (2) 34.955 (1) 34.955 (1) 22.309 (1) The superscript numbers within the parenthesis indicate the mode of buckling…”

Section: Effect Of Foundation Stiffness Coefficients On Critical Buckmentioning

confidence: 99%

“…(22) and the quadratic function form of in-plane loading into the stability Eq. (21) and applying the kinematic and constitutive relations, leads to the buckling equation as…”

Section: In-plane Loading Configurationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Stability analysis of functionally graded rectangular plates under nonlinearly varying in-plane loading resting on elastic foundation

Bodaghi

Saidi

2010

Arch Appl Mech

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“…Consequently, the material inhomogeneity on the stress concentration for FGM has attracted many researchers in the multidiscipline area of materials, machines, mechanics and applied mathematics. Based on the theory of complex variable functions, two-dimensional stress distribution of an FGM plate with a circular hole under arbitrary constant loads was derived by Yang et al [6]. Dineva et al [7] addressed the evaluation of the stress and electric field concentrations around a circular hole in a FGM piezoelectric plane subjected to anti-plane elastic SH-wave and in-plane time-harmonic electric load.…”

Section: Introductionmentioning

confidence: 99%

Stress field of a radially functionally graded panel with a circular elastic inclusion under static anti-plane shear loading

Shi

2015

J Mech Sci Technol

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The elastic stress field around a circular elastic inclusion in an infinite functionally graded material (FGM) panel that is subjected to a uniform static anti-plane shear loading at infinity is considered. Assuming the rigidity modulus of the FGM panel to be exponential, the analytical solutions of stress and strain distribution around the circular elastic inclusion are obtained by using the variable separation method. Due the generality of the elastic inclusion, other geometrical discontinuities, such as hole and rigid inclusion, can be seen as special cases of circular elastic inclusion when the inclusion rigidity modulus takes a suitable value. Therefore, the present solutions analytically reduce to some classical solution in some special cases. The present analytical solutions are compared with the existing exact solutions to verify them. Finally, the effects of the relative inclusion rigidity modulus ratio and the inhomogeneous rigidity modulus ratio on the stress distribution and the concentration factor are systematically investigated.

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“…They found that the stress concentration factor is reduced when Young's modulus progressively decreases towards the hole. Subsequently, Yang et al (2009) investigated the stress field around a circular hole in a FGM plate. They used piece-wise homogeneous layers and complex variable methods.…”

Section: Introductionmentioning

confidence: 99%

Stress concentration around a hole in a radially inhomogeneous plate

Mohammadi

Dryden

Jiang

2011

International Journal of Solids and Structures

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a b s t r a c tThe stress concentration factor around a circular hole in an infinite plate subjected to uniform biaxial tension and pure shear is considered. The plate is made of a functionally graded material where both Young's modulus and Poisson's ratio vary in the radial direction. For plane stress conditions, the governing differential equation for the stress function is derived and solved. A general form for the stress concentration factor in case of biaxial tension is presented. Using a Frobenius series solution, the stress concentration factor is calculated for pure shear case. The stress concentration factor for uniaxial tension is then obtained by superposition of these two modes. The effect of nonhomogeneous stiffness and varying Poisson's ratio upon the stress concentration factors are analyzed. A reasonable approximation in the practical range of Young's modulus is obtained for the stress concentration factor in pure shear loading.

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Stress analysis of a functional graded material plate with a circular hole

Cited by 76 publications

References 26 publications

Stability analysis of functionally graded rectangular plates under nonlinearly varying in-plane loading resting on elastic foundation

Stability analysis of functionally graded rectangular plates under nonlinearly varying in-plane loading resting on elastic foundation

Stress field of a radially functionally graded panel with a circular elastic inclusion under static anti-plane shear loading

Stress concentration around a hole in a radially inhomogeneous plate

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