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.
Skip Nav Destination
e-mail: yin@civil.columbia.edu
Article navigation
March 2011
Research Papers
Elastic Green’s Functions for a Specific Graded Material With a Quadratic Variation of Elasticity
Zifeng F. Yuan,
Zifeng F. Yuan
Department of Civil Engineering and Engineering Mechanics,
Columbia University
, 610 SW Mudd, 500 West 120th Street, New York, NY 10027
Search for other works by this author on:
Huiming M. Yin
Huiming M. Yin
Department of Civil Engineering and Engineering Mechanics,
e-mail: yin@civil.columbia.edu
Columbia University
, 610 SW Mudd, 500 West 120th Street, New York, NY 10027
Search for other works by this author on:
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 10027e-mail: yin@civil.columbia.edu
J. Appl. Mech. Mar 2011, 78(2): 021021 (6 pages)
Published Online: December 20, 2010
Article history
Received:
January 21, 2010
Revised:
September 20, 2010
Posted:
September 24, 2010
Published:
December 20, 2010
Online:
December 20, 2010
Citation
Yuan, Z. F., and Yin, H. M. (December 20, 2010). "Elastic Green’s Functions for a Specific Graded Material With a Quadratic Variation of Elasticity." ASME. J. Appl. Mech. March 2011; 78(2): 021021. https://doi.org/10.1115/1.4002615
Download citation file:
Get Email Alerts
Hamiltonian System-Based Symplectic Framework for Analytical Vibration Analysis of Microplates
J. Appl. Mech (December 2024)
Related Articles
The Role of Beam Flexibility and Ground Contact Model in the Clattering of Deformable Beams
J. Dyn. Sys., Meas., Control (June,2004)
Isoparametric Graded Finite Elements for Nonhomogeneous Isotropic and Orthotropic Materials
J. Appl. Mech (July,2002)
Parametric Formulation of the Finite-Volume Theory for Functionally Graded Materials—Part I: Analysis
J. Appl. Mech (September,2007)
Related Proceedings Papers
Related Chapters
Spring Constants of Elastic Shapes in Contact
Applying the ASME Codes: Plant Piping & Pressure Vessels (Mister Mech Mentor, Vol. 2)
Elastic Constant Used in Continuum-Based Adhesion Models
International Symposium on Information Engineering and Electronic Commerce, 3rd (IEEC 2011)
Monocrystal-Polycrystal Elastic-Constant Models
Dynamic Elastic Modulus Measurements in Materials