An analytical approach for stress analysis of functionally graded annular sector plates

Jomehzadeh, E.; Saidi, A.R.; Atashipour, Seyed Rasoul

doi:10.1016/j.matdes.2009.02.011

Cited by 79 publications

(30 citation statements)

References 20 publications

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“…(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%

“…Bending analysis of a simply supported FG plate under transverse load using both two-dimensional trigonometric and three-dimensional elasticity solutions was investigated by Zenkour [20]. 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.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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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“…(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%

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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“…To eliminate this deficiency, the FSDT was developed then, which assumes constant states of the transverse shear stresses through the plate thickness. There is also a great deal of research on the plate structure on the basis of FSDTs [11][12][13][14][15][16][17][18][19][20][21][22][23]. Generally, the shear correction factor is used to adjust the transverse shear stiffness as a constant, which differs from the fact that the shear correction factor is determined by the material properties and boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

A modified Fourier solution for vibration analysis of moderately thick laminated annular sector plates with general boundary conditions, internal radial line and circumferential arc supports

Pang

Miao³

et al. 2017

Curved and Layered Structures

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Abstract:In this paper, a modified Fourier solution based on the first-order shear deformation theory is developed for the free vibration problem of moderately thick composite laminated annular sector plates with general boundary conditions, internal radial line and circumferential arc supports. In this solution approach, regardless of boundary conditions, the displacement and rotation components of the sector plate are written in the form of the trigonometric series expansion in which several auxiliary terms are added to ensure and accelerate the convergence of the series. Each of the unknown coefficients is taken as the generalized coordinate and determined using the RaleighRitz method. The accuracy and reliability of the present solution are validated by the comparison with the results found in the literature, and numerous new results for composite laminated annular sector plates considering various kinds of boundary conditions are presented. Comprehensive studies on the effects of elastic restraint parameters, layout schemes and locations of line/arc supports are also made. New results are obtained for laminated annular sector plates subjected to elastic boundary restraints and arbitrary internal radial line and circumferential arc supports in both directions, and they may serve as benchmark solutions for future researches.

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“…Jomehzadeh et al examined the bending of a part of FGM annular sector plates using the first order shear deformation plate theory as the structure dimensions diminish in the micro scale, the effect of structure size plays a significant role in the correct examination of such structures in minute scales [24]. Also, Asghari et al [25,26] investigated the size-dependent behavior of FGM micro beams using the modified couple stress theory and the Euler-Bernoulli and Timoshenko beam models.…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of functionally graded stiffened micro-cylinder based on the modified couple stress theory

Jabbarian

Ahmadian

2017

Scientia Iranica

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Abstract. In this paper, free vibration of the micro-cylinder made by functionally graded material that is stiffened in circumferential direction, has been investigated based on the modified couple stress and first order shear deformation theories. Modified couple stress theory (MCST) has been used to catch size effects in micro scales. By using first order shear deformation theory and Hamilton principle, general equations of motion and corresponding boundary conditions have been derived. Free vibration of the structure has been investigated by implementing simply supported boundary condition as a common case. The effects of different parameters such as dimensionless length scale parameter, distribution of FGM properties, number of stiffeners, thickness and length on the natural frequencies were calculated and compared with classical continuum theory. Results show that effects of the size are considerable and also using stiffeners lead to increase in natural frequencies which is because of increase in stiffness of the cylinder.

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An analytical approach for stress analysis of functionally graded annular sector plates

Cited by 79 publications

References 20 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

A modified Fourier solution for vibration analysis of moderately thick laminated annular sector plates with general boundary conditions, internal radial line and circumferential arc supports

Free vibration analysis of functionally graded stiffened micro-cylinder based on the modified couple stress theory

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