Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-27T12:03:05.012Z Has data issue: false hasContentIssue false
  • English
  • Français

Punch Problem for Planar Anisotropic Elastic Half-Plane

Published online by Cambridge University Press:  16 June 2011

R.-L. Lin
R.-L. Lin*
Affiliation:
Department of Mechanical Engineering, Southern Taiwan University, Tainan, Taiwan 71008, R.O.C.
*
*Associate Professor, corresponding author
Get access

Abstract

The two dimensional punch problem for planar anisotropic elastic half-plane is revisited using the Lekhnitskii's formulation with aid of the Fourier transform and boundary integral equation. Four different conditions of contact problem for the rigid punch are analyzed in this study. From the combination of surface Green's function of half-plane and Hooke's law of anisotropic material, a set of Fredholm integral equations are obtained for mixed boundary value problems. After solving the integral equation according to specified contact condition, the explicit distributions of surface traction under the punch are obtained in closed-form. From the surface traction and Green's function of anisotropic half-plane, the full-field solutions of stresses are constructed. Numerical calculations of surface traction under the rigid punch are presented base on the analysis and are discussed in detail.

Keywords

Rigid punchPlanar anisotropicIntegral equation
Type
Articles
Information
Journal of Mechanics , Volume 27 , Issue 2 , June 2011 , pp. 215 - 226
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2011

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1. Lekhnitskii, S. G.Theory of Elasticity of an Anisotropic Body, Holden Day, San Francisco (1963).Google Scholar
2. Stroh, A. N. “Dislocations and Cracks in Anisotropic Elasticity,” Philosophical Magazine, 7, pp. 625–646 (1958).CrossRefGoogle Scholar
3. Ting, T. C. T., Anisotropic Elasticity: Theory and Application, Oxford University Press, Oxford (1996).CrossRefGoogle Scholar
4. Ma, C. C. and Lin, R. L. “Full Field Analysis of Planar Anisotropic Layered Half-Plane for Concentrated Forces and Edge Dislocations,” Procceding of the Royal society of London, 458, pp. 2369–2392 (2002).CrossRefGoogle Scholar
5. Muskhelishvili, N. I.Some Basic Problems of the Mathematical Theory of Elasticiy, Leydon, Noordhoff (1953).Google Scholar
6. Green, A. E. and Zerna, W.Theoretical Elasiticity, Clarendon Press, Oxford, U.K (1954).Google Scholar
7. Gladwell, G. M. L., Contact Problems in the Classical Theory of Elasticity, Sijthoff and Noordhoff, The Netherlands (1980).CrossRefGoogle Scholar
8. Johnson, K. L.Contact Mechanics, Cambridge University Press, Cambridge, U.K (1985).CrossRefGoogle Scholar
9. Klintworth, J. W. and Stronge, W. J. “Plane Punch Indentation of Anisotropic Elastic Half Space,” Journal of Applied Mechanics, ASME, 57, pp. 84–90 (1990).CrossRefGoogle Scholar
10. Fan, H. and Keer, L. M. “Two-Dimensional Contact on an Anisotropic Elastic Half-Space,” Journal of Applied of Mechanics, ASME, 61, pp. 250–255 (1994).CrossRefGoogle Scholar
11. Fan, C. W. and Hwu, C. B. “Punch Problems for an Anisotropic Elastic Half-Plane,” Journal of Applied of Mechanics, ASME, 63, pp. 69–76 (1996).CrossRefGoogle Scholar
12. Hwu, C. B. and Fan, C. W. “Sliding Punches with or without Friction along the Surface of an Anisotropic Elastic Half-Plane,” Quarterly Journal of Mechanics and Applied Mathematics, 51, pp. 159–177 (1998).CrossRefGoogle Scholar
13. Chao, C. K., Wu, S. P. and Gao, B. “Thermoelastic Contact Between a Flat Punch and an Anisotropic Half-Space,” Journal of Applied Mechanics, ASME, 66, pp. 548–552 (1999).CrossRefGoogle Scholar
14. Ciavarella, M. “Indentation by Normally Flat or Conical Indenters with Rounded Corners,” International Journal of Solids and Structures, 36, pp. 4149–4181 (1999).CrossRefGoogle Scholar
15. Fu, G. and Chandra, A. “Normal Indentation of Elastic Half-Space with a Rigid Frictionless Axisymmetric Punch,” Journal of Applied Mechanics, ASME, 69, pp. 142–147 (2002).CrossRefGoogle Scholar
16. Porter, M. I. and Hills, D. A. “Note on the Complete Contact Between a Flat Rigid Punch and an Elastic Layer Attached to a Dissimilar Substrate,” International Journal of Mechanical Sciences, 47, pp. 509–520 (2002).CrossRefGoogle Scholar
17. Wang, J. H.Chen, C. Q. and Lu, T. J. “Indentation Responses of Piezoelectric Films,” Journal of the Mechanics and Physics of Solids, 56, pp. 3331–3351 (2008).CrossRefGoogle Scholar
18. Comez, I. “Frictional Contact Problem for a Rigid Cylindrical Stamp and an Elastic Layer Resting on a Half-Plnae,” International Journal of Solids and Structures, 47, pp. 1090–1097 (2010).CrossRefGoogle Scholar