Theoretical formulation, Navier's solutions of rectangular plates, and finite element models based on the third-order shear deformation plate theory are presented for the analysis of through-thickness functionally graded plates. The plates are assumed to have isotropic, two-constituent material distribution through the thickness, and the modulus of elasticity of the plate is assumed to vary according to a power-law distribution in terms of the volume fractions of the constituents. The formulation accounts for the thermomechanical coupling, time dependency, and the von Karman-type geometric non-linearity. Numerical results of the linear third-order theory and non-linear first-order theory are presented to show the effect of the material distribution on the deflections and stresses. Copyright © 2000 John Wiley & Sons, Ltd.

Analysis of functionally graded plates

This paper presents a review of the principal developments in functionally graded materials (FGMs) with an emphasis on the recent work published since 2000. Diverse areas relevant to various aspects of theory and applications of FGM are reflected in this paper. They include homogenization of particulate FGM, heat transfer issues, stress, stability and dynamic analyses, testing, manufacturing and design, applications, and fracture. The critical areas where further research is needed for a successful implementation of FGM in design are outlined in the conclusions. DOI: 10.1115/1.2777164

https://web.mst.edu/~vbirman/papers/Modeling%20and%20Analysis%20of%20FGM_Review_2007.pdf

Modeling and Analysis of Functionally Graded Materials and Structures

Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments

A critical review of recent research on functionally graded plates

A new beam finite element for the analysis of functionally graded materials

Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates

The pseudodynamic thermoelastic response of functionally graded ceramic-metal cylinders is studied. This paper presents the finite-element formulation of the 1D, axisymmetric heat transfer equation and the thermoelastic radial boundary value problem. A two-step solution of the governing equations of thermoelasticity is presented. Thermoelastic coupling is considered by taking into effect the temperature dependence of the constitutive equations. Nonlinearity due to the temperature dependence of the material properties of the constituent ceramic and metal is considered. A parametric study with respect to varying volume fraction of the metal is conducted. Temperature and radial/hoop stress distributions arising due to rapid heating of the inner surface of the functionally graded cylinder are presented.

Thermoelastic analysis of functionally graded ceramic-metal cylinder

Cross-ply laminates with transverse plies containing through-width matrix cracks across the thickness of the transverse plies are studied using an energy-based approach,complementary to that of Hashin. An upper bound on the effective axial stiffness of the cracked laminates with a uniform distribution of transverse cracks is derived. The equations governing the field variables in a typical RVE are derived using thelayerwise laminate theory of Reddy and are solved using the finite element method. The predicted reduction in the effective axial modulus is in good agreement with experimental results, and it approaches a fixed value with increase in crack density for laminates with bothstaggered andnon-staggered cracking. Laminates with staggered cracks showed a greater reduction in effective modulus at lower crack densities. The stress distribution and mechanics of load transfer is examined in detail, at two crack densities including the characteristic damage state. The crack opening profile has been normalized in a special way in terms of the crack density, layup parameters and material properties.

Transverse matrix cracks in cross-ply laminates: Stress transfer, stiffness reduction and crack opening profiles

Cross-ply laminates with transverse matrix cracks are studied using the variational approach. An upper bound on the reduced stiffness has been derived, complementary to Hashin’s lower bound, for a given density of matrix cracks. Staggerring in crack patterns is also considered. The associated elasticity problem is solved using the Layerwise Laminate Theory of Reddy. The effect of crack density on the crack opening displacements and stress transfer is examined.

G. N. Praveen

Papers

Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates

Thermoelastic analysis of functionally graded ceramic-metal cylinder

Transverse matrix cracks in cross-ply laminates: Stress transfer, stiffness reduction and crack opening profiles

Stiffness Reduction in Composite Laminates due to Transverse Matrix Cracks