Abstract
This paper investigates the interaction between a point heat source and a nonuniformly coated circular inclusion under plane deformation. Based on the complex variable theory and conformal mapping in conjunction with the analytical continuation method, the general expressions of the temperature, displacements, and stresses for three dissimilar media are derived explicitly in a series form. Numerical results are provided for some particular examples to investigate the effect of material combinations on the interfacial stresses. The derived analytical solution can also be used as a fundamental solution for the boundary element method as well as for other physical models, including welding and cutting.
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References
Dundurs J.: On the interaction of a screw dislocation with inhomogeneities. Recent Adv. Eng. Sci 2, 223–233 (1967)
Kattis M.A., Meguid S.A.: Two-phase potentials for the treatment of an elastic inclusion in plane thermoelasticity. ASME J. Appl. Mech 62, 7–12 (1995)
Wu L., Markenscoff X.: Asymptotics for thin elastic ligaments with applications to body force and thermal loadings. J. Mech. Phys. Solids 45, 2033–2054 (1997)
Yoshikawa K., Hasebe N.: Heat source in infinite plane with elliptic rigid inclusion and hole. J. Eng. Mech. 125, 684–691 (1999)
Wang C.H., Chao C.K.: Green’s function for a point heat source in an anisotropic body containing an elliptic hole or a rigid inclusion. Chin. J. Mech. 15, 89–95 (1999)
Christensen R.M., Lo K.H.: Solution for effective shear properties in three phase sphere and cylinder models. J. Mech. Phys. Solids 27, 315–330 (1979)
Xiao Z.M., Chen B.J.: On the interaction between an edge dislocation and a coated inclusion. Int. J. Solids Struct. 38, 2533–2548 (2001)
Chen F.M.: Edge dislocation interacting with a nonuniformly coated circular inclusion. Arch. Appl. Mech. 81, 1117–1128 (2011)
Chao C.K., Chen F.M., Shen M.H.: Green’s functions for a point heat source in circularly cylindrical layered media. J. Therm. Stress. 29, 809–847 (2006)
Chao C.K., Chen F.M., Shen M.H.: An exact solution for thermal stresses in a three-phase composite subject to uniform heat flow. Int. J. Solids Struct. 44, 926–940 (2007)
Chao C.K.: Thermal stresses in a viscoelastic trimaterial. Acta Mech. 32, 623–655 (2010)
Muskhelishvili N.I.: Some Basic Problems of Mathematical Theory of Elasticity. Noordhoff, Groningen (1953)
Schinzinger R., Laura P.A.A.: Conformal Mapping: Methods and Applications. Elsevier, New York (1991)
Ozisik M.N.: Heat Conduction. Wiley, New York (1980)
Chao C.K., Lu M.L., Chen F.M.: Interaction between a nonuniformly coated circular inclusion and a remote uniform heat flow. J. Therm. Stress. 35, 118–137 (2012)
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Chen, F.M., Lai, J.Y. Interaction between a point heat source and a nonuniformly coated circular inclusion. Acta Mech 224, 2089–2106 (2013). https://doi.org/10.1007/s00707-013-0879-1
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DOI: https://doi.org/10.1007/s00707-013-0879-1