Three-Dimensional Flexure of Rectangular Plates Made of Functionally Graded Materials

2005 ◽  
Vol 72 (5) ◽  
pp. 788-791 ◽  
Author(s):  
Isaac Elishakoff ◽  
Cristina Gentilini
Keyword(s):  
Functionally Graded Materials ◽  
Power Law ◽  
Minimum Energy ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Power Law Distribution ◽  
Dimensional Solution ◽  
Energy Principle ◽  
Graded Materials

A three-dimensional solution for the problem of transversely loaded, all-round clamped rectangular plates of arbitrary thickness is presented within the linear, small deformation theory of elasticity. The Ritz minimum energy principle is employed to derive the governing equation of the plate made of functionally graded materials. In theory, if we employ an infinite number of terms in the displacement series, the exact solution can be determined. However, a practical limit always exists due to numerical implementation. The solution has a validity comparable to some higher order theories. A power-law distribution for the mechanical characteristics is adopted to model the continuous variation of properties from those of one component to those of the other. The displacements and stresses of the plate for different values of the power-law exponent are investigated.

Vibrational behavior of beams made of functionally graded materials by using a mixed formulation

2020 ◽  
Vol 234 (18) ◽  
pp. 3650-3666 ◽  
Author(s):  
Souhir Zghal ◽  
Fakhreddine Dammak
Keyword(s):  
Functionally Graded Materials ◽  
Power Law ◽  
Transverse Shear ◽  
Volume Fraction ◽  
Functionally Graded ◽  
Mixed Formulation ◽  
Shear Stresses ◽  
Power Law Distribution ◽  
Graded Materials ◽  
Vibrational Behavior

This paper investigates the vibrational behavior of beams made of functionally graded materials using a mixed formulation. Unlike the other high order shear deformation theories (HSDTs), the proposed formulation is elaborated within a double field of displacements and stresses which offers the possibility of the development of low order linear elements with enhanced accuracy. As well as, the effect of the transverse shear strains and the zero condition of the transverse shear stresses on the top and bottom surfaces are verified. The material characteristics of the beams are described via a power law distribution in order to take into account the continuous variation of the volume fraction of its constituents along the thickness direction. Numerical simulations are conducted to show the influence of power law index, slenderness ratios, and boundary conditions on natural frequencies of functionally graded beams. Results demonstrate the efficiency and the applicability of the model based on a refined mixed formulation and its ability to predict the vibrational behavior of functionally graded beams with good accuracy.

Numerical Investigation on the Fracture Behaviors of Three-Dimensional Functionally Graded Materials

2007 ◽  
Vol 353-358 ◽  
pp. 1098-1101 ◽  
Author(s):  
Hong Jun Yu ◽  
Li Cheng Guo ◽  
Lin Zhi Wu
Keyword(s):  
Functionally Graded Materials ◽  
Crack Front ◽  
Material Properties ◽  
High Efficiency ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Parameter Analysis ◽  
Graded Materials ◽  
Gaussian Integration ◽  
Fracture Behaviors

Functionally graded materials (FGMs) with continuous varying properties have absorbed great attention for the purpose of eliminating the mismatch of material properties which may result in cracking. In this paper, three-dimensional finite element method (3D FEM) based on nonhomogeneous elements is used to study the fracture behaviors of a 3D FGM plate. Since real material properties at Gaussian integration points are adopted during forming the element stiffness matrix, the nonhomogeneous material properties can be applied in each element. Moreover, 20-node singular elements are used around the crack front to deal with the singularity of stress fields at the crack front. By this way, the stress intensity factors (SIFs) can be calculated with high efficiency and accuracy. Therefore, compared with the general FEM using homogeneouos elements, the calculating efficiency and accuracy can be increased. Finally, parameter analysis is conducted. It is found that the material nonhomogeneity constant and the crack parameter have significant influences on the SIFs.

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