Parametric Formulation of the Finite-Volume Theory for Functionally Graded Materials—Part I: Analysis

[+] Author and Article Information
Marcio A. Cavalcante, Severino P. Marques

Center of Technology, Federal University of Alagoas, Maceio, Alagoas, Brazil

Marek-Jerzy Pindera

Civil Engineering Department, University of Virginia, Charlottesville, VA 22903

J. Appl. Mech 74(5), 935-945 (Dec 22, 2006) (11 pages) doi:10.1115/1.2722312 History: Received June 06, 2006; Revised December 22, 2006

The recently reconstructed higher-order theory for functionally graded materials is further enhanced by incorporating arbitrary quadrilateral subcell analysis capability through a parametric formulation. This capability significantly improves the efficiency of modeling continuous inclusions with arbitrarily-shaped cross sections of a graded material’s microstructure previously approximated using discretization based on rectangular subcells, as well as modeling of structural components with curved boundaries. Part I of this paper describes the development of the local conductivity and stiffness matrices for a quadrilateral subcell which are then assembled into global matrices in an efficient manner following the finite-element assembly procedure. Part II verifies the parametric formulation through comparison with analytical solutions for homogeneous curved structural components and graded components where grading is modeled using piecewise uniform thermoelastic moduli assigned to each discretized region. Results for a heterogeneous microstructure in the form of a single inclusion embedded in a matrix phase are also generated and compared with the exact analytical solution, as well as with the results obtained using the original reconstructed theory based on rectangular discretization and finite-element analysis.

Copyright © 2007 by American Society of Mechanical Engineers
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Grahic Jump Location
Figure 2

Discretization of a square region containing a circular inclusion: (a) discretization based on 900 rectangular subcells; (b) discretization based on 500 quadrilateral subcells

Grahic Jump Location
Figure 1

Simplified discretization of a graded microstructure (left) into rectangular subcells with the local coordinate system x2(β)−x3(γ) (right) used in the reconstructed finite-volume theory

Grahic Jump Location
Figure 3

Mapping of the reference subcell in the η-ξ plane onto a quadrilateral subcell in the x-y plane of the actual microstructure.




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