A REFINED SHEAR DEFORMATION PLATE THEORY FOR STATIC AND FREE VIBRATION ANALYSIS OF FUNCTIONALLY GRADED PLATES

Öz

In this research, an efficient shear deformation plate theory  for a  functionally graded  plate  has been investigated by the use of the new four variable refined plate theory. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory account for higher-order variation of transverse shear strain through the depth of the plate and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Based on the  present  higher-order  shear  deformation  plate  theory,  the  equations  of  the  motion  are derived  from  Hamilton’s  principal. The plate faces are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity, Poisson’s ratio of the faces, and thermal expansion coefficients are assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. The validity of the present theory is investigated by comparing some of the present results with those of the classical, the first-order and the other higher-order theories. The influences played by the transverse shear deformation, aspect ratio, side-to-thickness ratio, and volume fraction distribution are studied. Numerical results for deflections and stresses of functionally graded plate are investigated.

Anahtar Kelimeler

• Functionally graded material,Static Analysis,Vibration Analysis,Modeling,Bending

A REFINED SHEAR DEFORMATION PLATE THEORY FOR STATIC AND FREE VIBRATION ANALYSIS OF FUNCTIONALLY GRADED PLATES

Öz

In this research, an efficient shear deformation plate theory  for a  functionally graded  plate  has been investigated by the use of the new four variable refined plate theory. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory account for higher-order variation of transverse shear strain through the depth of the plate and satisfies the zero traction boundary conditions on the surfaces of the plate without using shear correction factors. Based on the  present  higher-order  shear  deformation  plate  theory,  the  equations  of  the  motion  are derived  from  Hamilton’s  principal. The plate faces are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity, Poisson’s ratio of the faces, and thermal expansion coefficients are assumed to vary according to a power law distribution in terms of the volume fractions of the constituents. The validity of the present theory is investigated by comparing some of the present results with those of the classical, the first-order and the other higher-order theories. The influences played by the transverse shear deformation, aspect ratio, side-to-thickness ratio, and volume fraction distribution are studied. Numerical results for deflections and stresses of functionally graded plate are investigated.

Anahtar Kelimeler

• Functionally graded material,Static Analysis,Vibration Analysis,Modeling,Bending

Kaynakça

1. [1] J. N. Reddy, “Analysis of functionally graded plates,” Int. J. Num. Methods Eng., vol. 47, 2000, pp. 663-684. [2] Z.Q. Cheng, R.C. Batra, “Deflection Relationships Between the Homogeneous Kirchhoff Plate Theory and Different Functionally Graded Plate Theories, “Archives of Mechanics, vol. 52, 2000, pp. 143–158. [3] Z.Q. Cheng, R.C. Batra, “Exact Correspondence Between Eigenvalues of Membranes and Functionally Graded Simply Supported Polygonal Plates,” Journal of Sound and Vibration, vol. 229, 2000, pp. 879–895. [4] Z.Q. Cheng, R.C. Batra, “Three-dimensional Thermoelastic Deformations of a Functionally Graded Elliptic Plate,” Composites, Part B, vol. 31, 2000, pp. 97–106. [5] S.S.Vel, R.C. Batra, “Exact Solution for Thermoelastic Deformations of Functionally Graded Thick Rectangular Plates,” AIAA Journal, vol. 40, 2002, pp. 1421–1433.