0
Research Papers

Elastic Green’s Functions for a Specific Graded Material With a Quadratic Variation of Elasticity

[+] Author and Article Information
Zifeng F. Yuan

Department of Civil Engineering and Engineering Mechanics, Columbia University, 610 SW Mudd, 500 West 120th Street, New York, NY 10027

Huiming M. Yin

Department of Civil Engineering and Engineering Mechanics, Columbia University, 610 SW Mudd, 500 West 120th Street, New York, NY 10027yin@civil.columbia.edu

J. Appl. Mech 78(2), 021021 (Dec 20, 2010) (6 pages) doi:10.1115/1.4002615 History: Received January 21, 2010; Revised September 20, 2010; Posted September 24, 2010; Published December 20, 2010; Online December 20, 2010

In this work, Green’s functions for unbounded elastic domain in a functionally graded material with a quadratic variation of elastic moduli and constant Poisson’s ratio of 0.25 are derived for both two-dimensional (2D) and three-dimensional (3D) cases. The displacement fields caused by a point force are derived using the logarithmic potential and the Kelvin solution for 2D and 3D cases, respectively. For a circular (2D) or spherical (3D) bounded domain, analytical solutions are provided by superposing the above solutions and corresponding elastic general solutions. This closed form solution is valuable for elastic analysis with material stiffness variations caused by temperature, moisture, aging effect, or material composition, and it can be used to perform early stage verification of more complex models of functionally graded materials. Comparison of theoretical solution and finite element method results demonstrates the application and accuracy of this solution.

FIGURES IN THIS ARTICLE
<>
Copyright © 2011 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

A sketch of the graded material for the FEM model

Grahic Jump Location
Figure 2

A FEM model with ABAQUS : (a) the whole figure of the mesh and (b) a magnified mesh at the upper-right quarter of the central area

Grahic Jump Location
Figure 3

Comparison between FEM and theoretical results of: (a) displacement u2 in the gradation direction with x1=0 and (b) displacement u2 perpendicular to the gradation direction with x2=0

Grahic Jump Location
Figure 4

Comparison between FEM and theoretical results of (a) strain component ϵ1 and (b) strain component ϵ2 along gradation direction with x1=0

Grahic Jump Location
Figure 5

Comparison between FEM and theoretical results of: (a) displacement uz along gradation direction with ρ=0 and (b) displacement uz perpendicular to the gradation direction with z=0

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In