Three-dimensional elasticity solution for bending of functionally graded rectangular plates

Kashtalyan, Maria

doi:10.1016/s0997-7538(04)00053-1

Cited by 31 publications

(65 citation statements)

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“…In an analysis of FGM structures, partial differential equations with variable coefficients are presented which, in general, are difficult to solve analytically and only for some specific cases can analytical solutions be obtained [1][2][3][4][5] . As for more general problems, numerical methods such as finite element analysis can be used.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional analysis of functionally graded plate based on the Haar wavelet method

Chun

Zhong

2007

Acta Mech. Solida Sin.

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A three-dimensional analysis of a simply-supported functionally graded rectangular plate with an arbitrary distribution of material properties is made using a simple and effective method based on the Haar wavelet. With good features in treating singularities, Haar series solution converges rapidly for arbitrary distributions, especially for the case where the material properties change rapidly in some regions. Through numerical examples the influences of the ratio of material constants on the top and bottom surfaces and different material gradient distributions on the structural response of the plate to mechanical stimuli are studied.

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Section: Introductionmentioning

confidence: 99%

Three-dimensional analysis of functionally graded plate based on the Haar wavelet method

Chun

Zhong

2007

Acta Mech. Solida Sin.

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“…A three-dimensional elasticity solution developed by Kashtalyan [25] for analyzing of thick FG plates is used as the benchmark to measure the qualification of the present method. A moderately thick, simply supported FG plate of length a, width b = a and thickness h = a/3, is considered under a sinusoidal transverse loading in the form of q z (x, y) = q 0 sin (x) sin (y).…”

Section: Benchmark Problem and Its Numerical Solutionmentioning

confidence: 99%

“…Cheng and Batra [24] have related deflections of a simply supported functionally graded polygonal plate given by a TSDT and the first-order shear deformation theory (FSDT) to that of an equivalent homogeneous Kirchhoff plate. Kashtalyan [25] provided an exact solution to the three-dimensional deformations of a simply supported FG plate with exponential variation of Young's modulus through the thickness.…”

Section: Introductionmentioning

confidence: 99%

Bending analysis of thin functionally graded plates using generalized differential quadrature method

2011

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In this paper, the differential quadrature (DQ) method is presented for easy and effective analysis of isotropic functionally graded (FG) and functionally graded coated (FGC) thin plates with constant Poisson's ratio and varying Young's modulus in the thickness direction. The bending of FG and FGC plates under transverse loading has been studied using the polynomial differential quadrature (PDQ) and the harmonic differential quadrature (HDQ) methods. A three-dimensional elasticity solution for a moderately thick FG plate with exponential Young's modulus is used as the benchmark. Two examples, including a thin FG rectangular plate and a thin FGC rectangular plate with sigmoidal Young's modulus, are investigated. The numerical results of PDQ and HDQ methods reveal good agreement with other solutions. Also, it is shown that the formulations for thin FG plates and homogeneous plates are similar, except that the plane strain components of the middle surface in FG plates are not zero.

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“…Due to the hypotheses and simplification concerning the deformation field along the thickness direction, the applicability of the 2D plate theories is always confined to the plates with lower thickness-to-length ratios. To account for the deformation field as complete as possible, three-dimensional (3D) elasticity solutions were widely exploited for FGM plates [11][12][13][14][15][16][17][18][19][20] . Since the spatial variation of material properties, it is rather difficult to derive analytical solutions for FGM plate based on the 3D elasticity theory.…”

Section: Introductionmentioning

confidence: 99%

“…The common treatment was to assume z-dependent material properties and dealt with the through-thickness and in-plane direction separately. For example, the series expansions were used to derive an asymptotic solution in the thickness direction [11][12][13] , while the exponential law was also widely used to describe the variation of stiffness constants in the thickness direction and thus decouple the z-dependence from the governing equation [14][15][16][17][18] . The former encounters a large number of recurrence manipulations which causes low efficiency of calculation, while the synchronous exponential-law variations of all material properties are no more than the theoretical meaning.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional elasticity solutions for bending of generally supported thick functionally graded plates

张治成

张鹤

蒋吉清

2014

Appl. Math. Mech.-Engl. Ed.

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Three-dimensional elasticity solutions for static bending of thick functionally graded plates are presented using a hybrid semi-analytical approach-the state-space based differential quadrature method (SSDQM). The plate is generally supported at four edges for which the two-way differential quadrature method is used to solve the in-plane variations of the stress and displacement fields numerically. An approximate laminate model (ALM) is exploited to reduce the inhomogeneous plate into a multi-layered laminate, thus applying the state space method to solve analytically in the thickness direction. Both the convergence properties of SSDQM and ALM are examined. The SSDQM is validated by comparing the numerical results with the exact solutions reported in the literature. As an example, the Mori-Tanaka model is used to predict the effective bulk and shear moduli. Effects of gradient index and aspect ratios on the bending behavior of functionally graded thick plates are investigated.

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Three-dimensional elasticity solution for bending of functionally graded rectangular plates

Cited by 31 publications

References 0 publications

Three-dimensional analysis of functionally graded plate based on the Haar wavelet method

Three-dimensional analysis of functionally graded plate based on the Haar wavelet method

Bending analysis of thin functionally graded plates using generalized differential quadrature method

Three-dimensional elasticity solutions for bending of generally supported thick functionally graded plates

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