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Special Issue Honoring Professor Fazil Erdogan’s Contributions to Mixed Boundary Value Problems of Inhomogeneous and Functionally Graded Materials

A Parallel Domain Decomposition BEM Algorithm for Three-Dimensional Exponentially Graded Elasticity

[+] Author and Article Information
J. E. Ortiz, V. Mantič, R. Criado, F. París

Group of Elasticity and Strength of Materials, University of Seville, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain

W. A. Shelton

Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6367

L. J. Gray

Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6367; Group of Elasticity and Strength of Materials, University of Seville, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain

J. Appl. Mech 75(5), 051108 (Jul 11, 2008) (8 pages) doi:10.1115/1.2936232 History: Received June 15, 2007; Revised March 14, 2008; Published July 11, 2008

A parallel domain decomposition boundary integral algorithm for three-dimensional exponentially graded elasticity has been developed. As this subdomain algorithm allows the grading direction to vary in the structure, geometries arising from practical functionally graded material applications can be handled. Moreover, the boundary integral algorithm scales well with the number of processors, also helping to alleviate the high computational cost of evaluating the Green’s functions. For axisymmetric plane strain states in a radially graded material, the numerical results for cylindrical geometries are in excellent agreement with the analytical solution deduced herein.

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Copyright © 2008 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Domain decomposition mesh and boundary conditions for the graded parallelepiped

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Figure 2

The u1E0∕lσ0 displacement component for the graded parallelepiped

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Figure 3

The u3E0∕lσ0 displacement component for the graded parallelepiped

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Figure 4

The normal stress σ11∕σ0 for the graded parallelepiped

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Figure 5

Computation time versus number of processors for the graded parallelepiped

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Figure 6

Domain decomposition for the very thick hollow cylinder

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Figure 7

Computed values of urE(r0)∕r0p for β=0.75 and β=0 in the very thick hollow cylinder

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Figure 8

Computed values of σθ∕p for β=0.75 and β=0 in the very thick hollow cylinder

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Figure 9

Computed values of urE(r0)∕r0p for β=±0.75 in the thick hollow cylinder

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Figure 10

Computed values of σθ∕p for β=±0.75 in the thick hollow cylinder

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Figure 11

Computation time versus number of processors for the very thick hollow cylinder

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Figure 12

Geometry of a transversally isotropic carbon fiber embedded in an isotropic epoxy matrix with a radially graded interphase

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