An RMVT-based third-order shear deformation theory of multilayered functionally graded material plates

Chih-Ping Wu, Hao Yuan Li

Research output: Contribution to journalArticle

45 Citations (Scopus)

Abstract

A Reissner mixed variational theorem (RMVT)-based third-order shear deformation theory (TSDT) is developed for the static analysis of simply-supported, multilayered functionally graded material (FGM) plates under mechanical loads. The material properties of the FGM layers are assumed to obey either the exponent-law distributions through the thickness coordinate or the power-law distributions of the volume fractions of the constituents. In this theory, Reddy's third-order displacement model and the layerwise parabolic function distributions of transverse shear stresses are assumed in the kinematic and kinetic fields, respectively, a priori, where the effect of transverse normal stress is regarded as minor and thus ignored. The continuity conditions of both transverse shear stresses and elastic displacements at the interfaces between adjacent layers are then exactly satisfied in this RMVT-based TSDT. On the basis of RMVT, a set of Euler-Lagrange equations associated with the possible boundary conditions is derived. In conjunction with the method of variable separation and Fourier series expansion, this theory is successfully applied to the static analysis of simply-supported, multilayered FGM plates under mechanical loads. A parametric study of the effects of the material-property gradient index and the span-thickness ratio on the displacement and stress components induced in the plates is undertaken.

Original languageEnglish
Pages (from-to)2591-2605
Number of pages15
JournalComposite Structures
Volume92
Issue number10
DOIs
Publication statusPublished - 2010 Sep 1

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Functionally graded materials
Shear deformation
Static analysis
Shear stress
Materials properties
Fourier series
Distribution functions
Volume fraction
Kinematics
Boundary conditions
Kinetics

All Science Journal Classification (ASJC) codes

  • Ceramics and Composites
  • Civil and Structural Engineering

Cite this

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abstract = "A Reissner mixed variational theorem (RMVT)-based third-order shear deformation theory (TSDT) is developed for the static analysis of simply-supported, multilayered functionally graded material (FGM) plates under mechanical loads. The material properties of the FGM layers are assumed to obey either the exponent-law distributions through the thickness coordinate or the power-law distributions of the volume fractions of the constituents. In this theory, Reddy's third-order displacement model and the layerwise parabolic function distributions of transverse shear stresses are assumed in the kinematic and kinetic fields, respectively, a priori, where the effect of transverse normal stress is regarded as minor and thus ignored. The continuity conditions of both transverse shear stresses and elastic displacements at the interfaces between adjacent layers are then exactly satisfied in this RMVT-based TSDT. On the basis of RMVT, a set of Euler-Lagrange equations associated with the possible boundary conditions is derived. In conjunction with the method of variable separation and Fourier series expansion, this theory is successfully applied to the static analysis of simply-supported, multilayered FGM plates under mechanical loads. A parametric study of the effects of the material-property gradient index and the span-thickness ratio on the displacement and stress components induced in the plates is undertaken.",
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An RMVT-based third-order shear deformation theory of multilayered functionally graded material plates. / Wu, Chih-Ping; Li, Hao Yuan.

In: Composite Structures, Vol. 92, No. 10, 01.09.2010, p. 2591-2605.

Research output: Contribution to journalArticle

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