0
ADDITIONAL TECHNICAL PAPERS

Three-Dimensional Green’s Functions in an Anisotropic Half-Space With General Boundary Conditions

[+] Author and Article Information
E. Pan

Structures Technology, Inc. 543 Keisler Drive, Cary, NC 27511

J. Appl. Mech 70(1), 101-110 (Jan 23, 2003) (10 pages) doi:10.1115/1.1532570 History: Received February 19, 2001; Revised March 05, 2002; Online January 23, 2003
Copyright © 2003 by ASME
Your Session has timed out. Please sign back in to continue.

References

Barber, J. R., 1992, Elasticity, Kluwer Academic Publishers, Dordrecht, The Netherlands.
Ting, T. C. T., 1996, Anisotropic Elasticity, Oxford University Press, Oxford, UK.
Davis, R. O., and Selvadurai, A. P. S., 1996, Elasticity and Geomechanics, Cambridge University Press, Cambridge, MA.
Barnett,  D. M., and Lothe,  J., 1975, “Line Force Loadings on Anisotropic Half-Spaces and Wedges,” Phys. Norv., 8, pp. 13–22.
Mura, T., 1987, Micromechanics of Defects in Solids, 2nd Ed., Martinus Nijhof, Dordrecht, The Netherlands.
Vlassak,  J. J., and Nix,  W. D., 1994, “Measuring the Elastic Properties of Anisotropic Materials by Means of Indentation Experiments,” J. Mech. Phys. Solids, 42, pp. 1223–1245.
Liao,  J.J., and Wang,  C. D., 1998, “Elastic Solutions for a Transversely Isotropic Half-Space Subjected to a Point Load,” Int. J. Numer. Analyt. Meth. Geomech., 22, pp. 425–447.
Wang,  C. D., and Liao,  J. J., 1999, “Elastic Solutions for a Transversely Isotropic Half-Space Subjected to Buried Asymmetric-Loads,” Int. J. Numer. Analyt. Meth. Geomech., 23, pp. 115–139.
Willis,  J. R., 1966, “Hertzian Contact of Anisotropic Bodies,” J. Mech. Phys. Solids, 14, pp. 163–176.
Gladwell, G. M. L., 1980, Contact Problems in the Classical Theory of Elasticity, Sithoff and Noordhoff, The Netherlands.
Barber,  J. R., and Ciavarella,  M., 2000, “Contact Mechanics,” Int. J. Solids Struct. 37, pp. 29–43.
Yu,  H. Y., 2001, “A Concise Treatment of Indentation Problems in Transversely Isotropic Half Spaces,” Int. J. Solids Struct., 38, pp. 2213–2232.
Mindlin,  R. D., 1936, “Force at a Point in the Interior of a Semi-Infinite Solid,” Physics (N.Y.), 7, pp. 195–202.
Pan,  Y. C., and Chou,  T. W., 1979, “Green’s Function Solutions for Semi-Infinite Transversely Isotropic Materials,” Int. J. Eng. Sci. 17, pp. 545–551.
Barber,  J. R., and Sturla,  F. A., 1992, “Application of the Reciprocal Theorem to Some Problems for the Elastic Half-Space” J. Mech. Phys. Solids, 40, pp. 17–25.
Wu,  K. C., 1998, “Generalization of the Stroh Formalism to 3-Dimensional Anisotropic Elasticity,” J. Elast., 51, pp. 213–225.
Pan,  E., and Yuan,  F. G., 2000, “Three-Dimensional Green’s Functions in Anisotropic Bimaterials,” Int. J. Solids Struct., 37, pp. 5329–5351.
Yu,  H. Y., Sanday,  S. C., Rath,  B. B., and Chang,  C. I., 1995, “Elastic Fields due to Defects in Transversely Isotropic Half Spaces,” Proc. R. Soc. London, Ser. A, A449, pp. 1–30.
Dundurs,  J., and Hetenyi,  M., 1965, “Transmission of Force Between Two Semi-Infinite Solids,” ASME J. Appl. Mech., 32, pp. 671–674.
Fabrikant, I., 1989, Applications of Potential Theory in Mechanics: A Selection of New Results, Kluwer Academic Publishers, Dordrecht, The Netherlands.
Fabrikant, V. I., 1991, Mixed Boundary Value Problems of Potential Theory and Their Applications in Engineering, Kluwer Academic Publishers, Dordrecht, The Netherlands.
Craig, R. F., 1992, Soil Mechanics, 5th Ed., Chapman & Hall, New York.
Timoshenko, S., and Woinowsky-Krieger, S., 1987 Theory of Plates and Shells, 2nd Ed., McGraw-Hill, New York.
Shilkrot,  L. E., and Srolovitz,  D. J., 1998, “Elastic Analysis of Finite Stiffness Bimaterial Interfaces: Application to Dislocation-Interface Interactions,” Acta Mater., 46, pp. 3063–3075.
Gharpuray,  V. M., Dundurs,  J., and Keer,  L. M., 1991, “A Crack Terminating at a Slipping Interface Between Two Materials,” ASME J. Appl. Mech., 58, pp. 960–963.
Davies,  J. H., and Larkin,  I. A., 1994, “Theory of Potential Modulation in Lateral Surface Superlattices,” Phys. Rev. B, B49, pp. 4800–4809.
Larkin,  I. A., Davies,  J. H., Long,  A. R., and Cusco,  R., 1997, “Theory of Potential Modulation in Lateral Surface Superlattices, II. Piezoelectric Effect,” Phys. Rev. B, B56, pp. 15,242–15,251.
Holy,  V., Springholz,  G., Pinczolits,  M., and Bauer,  G., 1999, “Strain Induced Vertical and Lateral Correlations in Quantum Dot Superlattices,” Phys. Rev. Lett., 83, pp. 356–359.
Ru,  C. Q., 1999, “Analytic Solution for Eshelby’s Problem of an Inclusion of Arbitrary Shape in a Plane or Half-Plane,” ASME J. Appl. Mech., 66, pp. 315–322.
Ru,  C. Q., 2000, “Eshelby’s Problem for Two-Dimensional Piezoelectric Inclusion of Arbitrary Shapem,” Proc. R. Soc. London, Ser. A, A456, pp. 1051–1068.
Eshelby,  J. D., 1957, “The Determination of the Elastic Field on an Ellipsoidal Inclusion, and Related Problems,” Proc. R. Soc. London, Ser. A, A241, pp. 376–396.
Ting,  T. C. T., 2000, “Recent Developments in Anisotropic Elasticity,” Int. J. Solids Struct., 37, pp. 401–409.
Ting, T. C. T., 2001, “The Wonderful World of Anisotropic Elasticity—An Exciting Theme Park to Visit,” Proc. 4th Pacific International Conference on Aerospace Science and Technology,” pp. 1–7.
Ting,  T. C. T., and Wang,  M. Z., 1992, “Generalized Stroh Formalism for Anisotropic Elasticity for General Boundary Conditions,” Acta Mech. Sin., 8, pp. 193–207.
Wang,  M. Z., Ting,  T. C. T., and Yan,  G., 1993, “The Anisotropic Elastic Semi-Infinite Strip,” Q. Appl. Math., 51, pp. 283–297.
Tewary,  V. K., 1995, “Computationally Efficient Representation for Elastostatic and Elastodynamic Green’s Functions,” Phys. Rev. B, 51, pp. 15,695–15,702.
Ting,  T. C. T., and Lee,  V. G., 1997, “The Three-Dimensional Elastostatic Green’s Function for General Anisotropic Linear Elastic Solids,” Q. J. Mech. Appl. Math., 50, pp. 407–426.
Sales,  M. A., and Gray,  L. J., 1998, “Evaluation of the Anisotropic Green’s Function and its Derivatives,” Comput. Struct., 69, pp. 247–254.
Tonon,  F., Pan,  E., and Amadei,  B., 2001, “Green’s Functions and Boundary Element Method Formulation for 3D Anisotropic Media,” Comput. Struct., 79, pp. 469–482.
Pan,  E., 1997, “A General Boundary Element Analysis of 2-D Linear Elastic Fracture Mechanics,” Int. J. Fract., 88, pp. 41–59.
Pan, E., 2002, “Three-Dimensional Green’s Functions in Anisotropic Magneto-Electro-Elastic Bimaterials,” J. Appl. Math Phys., pp. 815–838.
Walker,  K. P., 1993, “Fourier Integral Representation of the Green’s Function for an Anisotropic Elastic Half-Space,” Proc. R. Soc. London, Ser. A, A443, pp. 367–389.
Love, A. E. H., 1994, A Treatise on the Mathematical Theory of Elasticity, 4th Ed., Dover Publication, New York.
Sokolnikoff, I. S., 1956, Mathematical Theory of Elasticity, McGraw-Hill, New York.
Hirth, J. P., and Lothe, J., 1982, Theory of Dislocations, 2nd Ed., John Wiley and Sons, New York.
Pan,  E., 1991, “Dislocation in an Infinite Poroelastic Medium,” Acta Mech., 87, pp. 105–115.
Paget,  D. F., 1981, “The Numerical Evaluation of Hadamard Finite-Part Intervals,” Numer. Math., 36, pp. 447–453.
Monegato,  G., 1994, “Numerical Evaluation of Hypersingular Integrals,” J. Comput. Appl. Math., 50, pp. 9–31.
Mastronardi,  N., and Occorsio,  D., 1996, “Some Numerical Algorithms to Evaluate Hadamard Finite-Part Integrals,” J. Comput. Appl. Math., 70, pp. 75–93.
Pan, E., and Yang, B., 2003, “Three-Dimensional Interfacial Green’s Functions in Anisotropic Bimaterials,” Appl. Math. Model., in press.

Figures

Grahic Jump Location
Variation of in-plane stress component σxx along the line x=y on the surface z=0, caused by the point force f =(0,0,1) and d =(0,0,1). Labels BC 1 to BC 8 correspond to the eight different sets of boundary conditions (2ah).
Grahic Jump Location
Variation of in-plane stress component σyy along the line x=y on the surface z=0, caused by the point force f =(0,0,1) at d =(0,0,1). Labels BC 1 to BC 8 correspond to the eight different sets of boundary conditions (2ah).
Grahic Jump Location
Variation of in-plane stress component σxx along the line x=y on the surface z=0, caused by the point force f =(1,0,0) at d =(0,0,1). Labels BC 1 to BC 8 correspond to the eight different sets of boundary conditions (2ah).
Grahic Jump Location
Variation of in-plane stress component σyy along the line x=y on the surface z=0, caused by the point force f =(1,0,0) at d =(0,0,1). Labels BC 1 to BC 8 correspond to the eight different sets of boundary conditions (2ah).

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