# Displacement Field Due to a Cylindrical Inclusion in a Thermoelastic Half-Space

Document Type: Research Paper

Authors

Department of Mathematics,Guru Jambheshwar ,University of Science & Technology, Hisar, Pin-125001, Haryana, India

Abstract

In this paper, the closed form analytical expressions for the displacement field due to a cylindrical inclusion in a thermoelastic half-space are obtained. These expressions are derived in the context of steady-state uncoupled thermoelasticity using thermoelastic displacement potential functions. The thermal displacement field is generated due to differences in the coefficients of linear thermal expansion between a subregion and the surrounding material. Further, comparison between displacement field in a half-space and in an infinite medium has been discussed. The variation of displacement field in a half-space and its comparison with an infinite medium is also shown graphically.

Keywords

### References

[1] Goodier J.N., 1937, On the integration of the thermoelastic equations, Philosophical Magazine 7(23):1017-1032.
[2] Mindlin R.D., Cheng, D.H., 1950, Thermoelastic stress in the semi-infinite solid, Journal of Applied Physics 21: 931-933.
[3] Yu H.Y., Sanday S.C., 1992, Centre of dilatation and thermal stresses in an elastic plate, Proceedings of the Royal Society of London A 438: 103-112.
[4] Hemayati M., Karami G., 2002, A boundary elements and particular integrals implementation for thermoelastic stress analysis, International Journal of Engineering Transactions A: Basics 15(2): 197-204.
[5] Nowinski J., 1961, Biharmonic solutions to the steady-state thermoelastic problems in three dimensions, Zeitschrift für Angewandte Mathematik und Physik ZAMP 12(2): 132-149.
[6] Wang M., Huang, K., 1991, Thermoelastic problems in the half space-An application of the general solution in elasticity, Applied Mathematics and Mechanics 12(9): 849-861.
[7] Seremet V., Bonnet G., Speianu T.,2009, New Poisson’s type integral formula for thermoelastic half-space, Hindawi Publishing Corporation, Mathematical Problems in Engineering 2009: 284380.
[8] Kedar G.D., Warbhe S.D., Deshmukh K.C., Kulkarni V.S., 2012,Thermal stresses in a semi-infinite solid circular cylinder, International Journal of Applied Mathematics and Mechanics 8(10): 38-46.
[9] Davies J.H., 2003, Elastic field in a semi-infinite solid due to thermal expansion or a coherently misfitting inclusion, Journal of Applied Mechanics 70(5): 655-660.
[10] Sen B., 1957, Note on a direct method of solving problems of elastic plates with circular boundaries having prescribed displacement, Zeitschrift für angewandte Mathematik und Physik ZAMP 8(4): 307-309.
[11] Arpaci V.S., 1984, Steady axially symmetric three-dimensional thermoelastic stresses in fuel roads, Nuclear Engineering and Design 80: 301-307.
[12] Rokne J., Singh B.M., Dhaliwal R.S., Vrbik J., 2003,The axisymmetric boussinesq-type problem for a half-space under optimal heating of arbitrary profile, International Journal of Mathematics and Mathematical Sciences 40: 2123-2131.
[13] Chao C.K., Chen F.M., Shen M.H., 2006, Green’s functions for a point heat source in circularly cylindrical layered media, Journal of Thermal Stresses 29(9): 809-847.
[14] Sadd M.H., 2005, Elasticity-Theory, Applications and Numerics, Elsevier Academic Press Inc., UK.
[15] Timoshenko S., Goodier J.N., 1951, Theory of Elasticity, McGraw-Hill, New York.