A theoretical analysis of FGM thin plates based on physical neutral surface

Zhang, Da-Guang; Zhou, Youhe

doi:10.1016/j.commatsci.2008.05.016

Cited by 281 publications

(124 citation statements)

References 21 publications

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“…Morimoto et al [36] and Abrate [37] noticed that there will be no stretching-bending coupling effect in constitutive equations if the reference surface is properly selected. Thereafter, based on physical neutral surface, Zhang and Zhou [38] and Zhang [39] carried out theoretical analyses to FGM plates and beams, respectively. They found that physical neutral surface theory has many merits in the engineering application due to its easiness and simplicity.…”

Section: Introductionmentioning

confidence: 99%

Non-Linear Bending of Functionally Graded Thin Plates with Different Moduli in Tension and Compression and Its General Perturbation Solution

Liu

et al. 2018

Applied Sciences

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Abstract:In this study, a set of Föppl-von Kármán equations for a bimodular functionally graded thin plate subjected to a uniformly distributed load is established, and its general perturbation solution in axisymmetric case is also obtained under different boundary conditions. First, the equation of equilibrium of the plate is established on the existence of the neutral layer when considering different properties in tension and compression. During the derivation of the consistency equation, the tensile effect in the thin plate with bimodular effect is fully taken into account. The perturbation method is used to solve the set of governing equations under different edge constraints, in which the central deflection and the load of the plate are taken as a perturbation parameter, respectively. The results indicate that the two selections for perturbation parameters are valid and consistent, and the two solutions are convenient for engineering application. This study also shows that the bimodular effect will modify the relation of load versus central deflection of the plate to some extent, and under the same edge constraint, the capacities resisting deformation in different cases of moduli depend on the relative magnitudes among the tensile modulus, the neutral layer modulus, and the compressive modulus.

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Section: Introductionmentioning

confidence: 99%

Non-Linear Bending of Functionally Graded Thin Plates with Different Moduli in Tension and Compression and Its General Perturbation Solution

Liu

et al. 2018

Applied Sciences

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show abstract

“…Therefore, stretching and bending deformations of FG plates are coupled. Some researchers [1,5,27] have shown that there is no stretchingbending coupling in constitutive equations if the origin of coordinate system is suitably selected in the thickness direction of the FG plate so as to be the neutral surface. To specify the position of neutral surface of FG plates, two different planes are considered for the measurement of z , namely, z ms and z ns , as depicted in Fig.…”

Section: Physical Neutral Surface Conceptmentioning

confidence: 99%

“…The situation of the neutral surface of the FG plate is determined to satisfy the first moment with respect to Young's modulus being zero as follows [5,27]: …”

Section: Physical Neutral Surface Conceptmentioning

confidence: 99%

“…Abrate [1] showed that there is no stretching-bending coupling in constitutive equations of FG plates, if the reference surface is properly selected. Zhang and Zhou [27] presented a theoretical analysis to the FG thin plates based on the physical neutral surface. They carried out the bending, buckling and free vibration analysis of simply supported rectangular and clamped circular FG plates.…”

Section: Introductionmentioning

confidence: 99%

“…Ref. [1,5,11,[19][20][21]27]). For instance, in the field of static analysis, Reddy et al [19] investigated the axisymmetric bending of functionally graded solid and annular circular plates.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Boundary element method applied to the bending analysis of thin functionally graded plates

Damanpack

Bodaghi

Ghassemi

et al. 2013

Lat. Am. j. solids struct.

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Application of biparametric perturbation method to functionally graded thin plates with different moduli in tension and compression

Yang

et al. 2019

Z Angew Math Mech

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In this study, a biparametric perturbation method is used for the solution of the large‐deflection bending problem of a functionally graded thin plate with different moduli in tension and compression. First, the Föppl‐von Kármán equations for the bimodular functionally graded thin plate are established in rectangular coordinates system, thus obtaining the axisymmetric simplified form in polar coordinates system. By adopting two groups of perturbation parameters, one group is gradient index and central deflection, another is gradient index and load, the biparametric perturbation solution for the established governing equations are obtained, respectively, under different boundary constrains. The result indicates that the two groups of parameter selections are valid, and the biparametric perturbation solution is also consistent to single‐parameter perturbation solution. The bimodular effects on stiffness and deformation of thin plates are also discussed via biparametric perturbation solutions obtained. The study indicates that the dominant factor influencing the stiffness is the relative magnitudes relation among the tensile modulus, the neutral layer modulus and the compressive modulus.

show abstract

A theoretical analysis of FGM thin plates based on physical neutral surface

Cited by 281 publications

References 21 publications

Non-Linear Bending of Functionally Graded Thin Plates with Different Moduli in Tension and Compression and Its General Perturbation Solution

Non-Linear Bending of Functionally Graded Thin Plates with Different Moduli in Tension and Compression and Its General Perturbation Solution

Boundary element method applied to the bending analysis of thin functionally graded plates

Application of biparametric perturbation method to functionally graded thin plates with different moduli in tension and compression

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