The novelty of this paper is to propose exact three-dimensional analytical solutions to the half infinite thermo-elastic body pressed by a rigid cylindrical structure for the first time, in which uniform heat flux flowing from rigid structure into the half infinite body is considered. Using recent general solutions expressed by four harmonic functions and extending potential theory method to consider heat effect, the governing integral equations are first derived. Then, the equations are analytically solved and displacement, stress, and temperature field components expressed by elementary functions are obtained. To validate the presented solutions, the correctness of the solutions is exactly examined, and normal contact displacement and stress without heat effect are compared with those in literatures. Furthermore, a numerical example which is the stainless steel thermo-elastic body pressed by a displacement restrictor is studied. Displacement, stress, and temperature distributions are analyzed, and the influence of heat flux on the pressed depth is also discussed in detail. The analytical solutions presented in this paper are rather important in engineering practice and can provide a basis for indentation analysis, displacement restrictor design, foundation settlement calculation, and so on.
LawnBWilshawR.Indentation fracture: principles and applications. J Mater Sci1975; 10: 1049–1081.
2.
MeyerEHugHJBennewitzR.Scanning probe microscopy: the lab on a tip. New York: Springer, 2013.
3.
SneddonIN.The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile. Int J Eng Sci1965; 3: 47–57.
4.
BarberJR.The solution of heated punch problems by point source methods. Int J Eng Sci1971; 9: 1165–1170.
5.
LevytskyVP.Interaction of rigid cylinder with elastic half-space by heat generation on the contact area. Int J Eng Sci1994; 32: 1693–1702.
6.
GrylitskyDVPaukVJ.Some quasistationary contact problems for half-space involving heat generation and radiation. Int J Eng Sci1995; 33: 1773–1781.
7.
BarberJR.Thermoelasticity and contact. J Therm Stress1999; 22: 513–525.
8.
YevtushenkoAAKulchytsky-ZhyhailoRD.Axi-symmetric steady-state contact problem for thermo-sensible heated bodies. Int J Eng Sci1999; 37: 1959–1972.
9.
RahmanM.The axisymmetric contact problem of thermoelasticity in the presence of an internal heat source. Int J Eng Sci2003; 41: 1899–1911.
10.
FabrikantVI.Applications of potential theory in mechanics: a selection of new results. Dordrecht: Kluwer Academic Publishers, 1989.
11.
FabrikantVI.Mixed boundary value problem of potential theory and their applications in engineering. Dordrecht: Kluwer Academic Publishers, 1991.
12.
ChenWQLeeKYDingHJ.General solution for transversely isotropic magneto-electro-thermo-elasticity and the potential theory method. Int J Eng Sci2004; 42: 1361–1379.
13.
ChenWQPanEWangHM, et al. Theory of indentation on multiferroic composite materials. J Mech Phys Solids2010; 58: 1524–1551.
14.
KarapetianEKalininSV.Indentation of a punch with chemical or heat distribution at its base into transversely isotropic half-space: application to local thermal and electrochemical probes. J Appl Phys2013; 113: 187201.
15.
YangJJinXY.Indentation of a flat circular punch with uniform heat flux at its base into transversely isotropic magneto-electro-thermo-elastic half space. J Appl Phys2014; 115: 083516.
16.
HuangYLXiaGZChenWQ, et al. Indentation of a transversely isotropic thermoporoelastic half-space by a rigid circular cylindrical punch. J Appl Mech2017; 84: 111001.
17.
WuFLiXYChenWQ, et al. Indentation on a transversely isotropic half-space of multiferroic composite medium with a circular contact region. Int J Eng Sci2018; 123: 236–289.
18.
ChenWQ.Some recent advances in 3D crack and contact analysis of elastic solids with transverse isotropy and multi-field coupling. Acta Mech Sinica2015; 31: 601–626.
19.
ChenWQZhuJLiXY.General solutions for elasticity of transversely isotropic materials with thermal and other effects: a review. J Therm Stress2019; 42: 90–106.
20.
KrenevLIAizikovichSMTokovyyYV, et al. Axisymmetric problem on the indentation of a hot circular punch into an arbitrarily nonhomogeneous half-space. Int J Solids Struct2015; 59: 18–28.
21.
VasilievASVolkovSSBelovAA, et al. Indentation of a hard transversely isotropic functionally graded coating by a conical indenter. Int J Eng Sci2017; 112: 63–75.
22.
HouPFZhangWHChenJY.Three-dimensional exact solutions of transversely isotropic coated structures under tilted circular flat punch contact. Int J Mech Sci2019; 151: 471–497.
23.
ArgatovI.A comparison of general solutions to the non-axisymmetric frictionless contact problem with a circular area of contact: when the symmetry does not matter. Symmetry2022; 14: 1083.
24.
ZemlyanovaAYWhiteLM.Axisymmetric frictionless indentation of a rigid stamp into a semi-space with a surface energetic boundary. Math Mech Solids2022; 27: 334–347.
25.
AbbasIAAbd-allaAN.Effects of thermal relaxations on thermoelastic interactions in an infinite orthotropic elastic medium with a cylindrical cavity. Arch Appl Mech2008; 78: 283–293.
26.
AbbasIA.A two-dimensional problem for a fibre-reinforced anisotropic thermoelastic half-space with energy dissipation. Sadhana2011; 36: 411–423.
27.
AbbasIAKumarR.2D deformation in initially stressed thermoelastic half-space with voids. Steel Compos Struct2016; 20: 1103–1117.
28.
AbbasIA.Analytical solution for a free vibration of a thermoelastic hollow sphere. Mech Based Des Struct Mach2015; 43: 265–276.
29.
AbbasIAAbdallaANAlzahraniFS, et al. Wave propagation in a generalized thermoelastic plate using eigenvalue approach. J Therm Stress2016; 39: 1367–1377.
30.
HobinyAAbbasI.A GN model on photothermal interactions in a two-dimensions semiconductor half space. Results Phys2019; 15: 102588.
31.
GhanmiAAbbasIA.An analytical study on the fractional transient heating within the skin tissue during the thermal therapy. J Therm Biol2019; 82: 229–233.
32.
YangJJinXYJinNG.A penny-shaped crack in transversely isotropic magneto-electro-thermo-elastic medium subjected to uniform symmetric heat flux. Int J Solids Struct2013; 51: 1792–1808.
33.
LiPDLiXYKangGZ.Axisymmetric thermo-elastic field in an infinite space containing a penny-shaped crack under a pair of symmetric uniform heat fluxes and its applications. Int J Mech Sci2016; 115–116: 634–644.
34.
LiXYLiPDKangGZ, et al. Steady-state thermo-elastic field in an infinite medium weakened by a penny-shaped crack: complete and exact solutions. Int J Solids Struct2016; 84: 167–182.
35.
HouPFJiangHYLiQH.Three-dimensional steady-state general solution for isotropic thermoelastic materials with applications I: general solutions. J Therm Stress2013; 36: 727–747.
36.
HouPFLiQHJiangHY.Three-dimensional steady-state general solution for isotropic thermoelastic materials with applications II: Green’s functions for two-phase infinite body. J Therm Stress2013; 36: 851–867.
37.
HouPFJiangHYTongJ, et al. Study on the coated isotropic thermoelastic material based on the three-dimensional Green’s function for a point heat source. Int J Mech Sci2014; 83: 155–162.
38.
LiQHHouPF.Three-dimensional Green’s functions for fluid and isotropic thermoelastic solid two-phase materials under heat loading. Case Stud Therm Eng2020; 20: 100631.
39.
LiQHHouPF.Three-dimensional quasi-static general solution for isotropic thermoelastic medium with applications. Case Stud Therm Eng2021; 25: 100897.
40.
KassirMKSihGC.Developments in theoretical and applied mechanics. Oxford: Pergamon Press, 1967.
41.
WilliamsWE.A solution of the steady-state thermoelastic equations. Z Angew Math Phys1961; 12: 452–455.
