Parametric Formulation of the Finite-Volume Theory for Functionally Graded Materials—Part II: Numerical Results

Author:

Cavalcante Marcio A. A.1,Marques Severino P. C.1,Pindera Marek-Jerzy2

Affiliation:

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

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

Abstract

In Part I of this communication, the finite-volume theory for functionally graded materials was further extended to enable efficient analysis of structural components with curved boundaries, as well as efficient modeling of continuous inclusions with arbitrarily-shaped cross sections of a graded material’s microstructure, previously approximated using discretizations by rectangular subcells. This was accomplished through a parametric formulation based on mapping of a reference square subcell onto a quadrilateral subcell resident in the actual microstructure. In Part II, the parametric formulation is verified through comparison with analytical solutions for homogeneous and graded curved structural components subjected to transient thermal and steady-state thermomechanical loading. 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 the matrix phase of large dimensions are also generated and compared with the exact analytical solution, as well as with the results obtained using the standard version of the finite-volume theory based on rectangular discretization and the finite-element method. It is demonstrated that the parametric finite-volume theory is a very competitive alternative to the finite-element method based on the quality of results and execution time.

Publisher

ASME International

Subject

Mechanical Engineering,Mechanics of Materials,Condensed Matter Physics

Reference16 articles.

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2. Efficient Reformulation of the Thermal Higher-Order Theory for FGM’s With Variable Thermal Conductivity;Zhong;Int. J. Comput. Eng. Sci.

3. Pindera, M-J., Bansal, Y., and Zhong, Y., 2004, “Finite-Volume Direct Averaging Theory for Functionally Graded Materials (FVDAT-FGM),” NASA Disclosure of Invention and New Technology Form 1679, September, 14, 2004.

4. Cavalcante, M. A. A. , 2006, “Modeling of the Transient Thermo-Mechanical Behavior of Composite Material Structures by the Finite-Volume Theory,” M.S. thesis, Civil Engineering Department, Federal University of Alagoas, Maceio, Alagoas, Brazil.

5. Transient Heat Conduction in Homogeneous and Non-Homogeneous Materials by the Laplace Transform Galerkin Boundary Element Method;Sutradhar;Eng. Anal. Boundary Elem.

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