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ORIGINAL PAPER
Two Dimensional Deformation of a Multilayered Thermoelastic Half-Space Due to Surface Loads and Heat Source
1
Department of Mathematics, Kurukshetra University, Kurukshetra, 136119, India
2
Department of Mathematics, Govt. College for Women, Bhodia Khera, Fatehabad, 125050, India
3
Department of Mathematics, Guru Jambheshwar University of Science and Technology, Hisar, 125001, India
Online publication date: 2020-03-12
Publication date: 2020-03-01
International Journal of Applied Mechanics and Engineering 2020;25(1):177-197
KEYWORDS
ABSTRACT
This article deals with a 2-D problem of quasi-static deformation of a multilayered thermoelastic medium due to surface loads and heat source. The propagator matrix is obtained for the multilayered formalism of thermoelastic layers. Analytical solutions, in terms of the displacements, stresses, heat flux and temperature function, are obtained for normal strip and line loads, shear strip and line loads and strip and line heat sources. Numerical computation of the obtained analytical expressions is also done. The effects of layering have been studied. For the verification of the results, results of earlier studies have been obtained as particular cases of the present study.
REFERENCES (41)
1.
Yang Y., Datcheva M. and Schanz T. (2016): Axisymmetric analysis of multilayered thermoelastic media with application to a repository for heat-emitting high-level nuclear waste in a geological formation. – Geophys. J. Int., vol.206, pp.1144-1161.
2.
Singh S.J. (1970): Static deformation of a multilayered half-space by internal sources. – J. Geophys. Res., vol.75, pp.3257–3263.
3.
Bache T.C. and Harkrider D.G. (1976): The body waves due to a general seismic source in a layered Earth model: 1 Formulation of the theory. – Bulletin of the Seismological Society of America, vol.66, No.6, pp.1805-1819.
4.
Small J.C. and Booker J.R. (1984): Finite layer analysis of layered elastic materials using a flexibility approach. Part 1-strip loadings. – International Journal for Numerical Methods in Engineering, vol.20, pp.1025-1037.
5.
Small J.C. and Booker J.R. (1986): Finite layer analysis of layered elastic materials using a flexibility approach. Part 2–circular and rectangular loadings. – Int. J. Numer. Methods Engg., vol.23, pp.959–978.
6.
Singh S.J. and Garg N.R. (1985): On two-dimensional elastic dislocations in a multilayered half-space. – Phys. Earth Planet. Inter., vol.40, pp.135–145.
7.
Garg N.R. and Singh S.J. (1987): 2-D static response of a transversely isotropic multilayered half-space to surface loads. – Indian J. Pure Appl. Math., vol.18, pp.763-777.
8.
Pan E. (1989): Static response of a transversely isotropic and layered half-space to general surface loads. – Phys. Earth Planet. Inter., vol.54, pp.353–363.
9.
Pan E. (1989): Static response of a transversely isotropic and layered half-space to general dislocation sources. – Phys. Earth Planet. Inter., vol.58, pp.103–117.
10.
Garg N.R., Singh S.J. and Manchanda S. (1991): Static deformation of an orthotropic multilayered elastic half-space by two-dimensional surface loads. – Proc. Indian Acad. Sci. (Earth Planet. Sci.), vol.100, No.2, pp.205-218.
11.
Garg N.R., Singh S.J. and Rani, S. (1992): Static deformation of a stratified medium by surface loads. – Indian J. Pure Math., vol.23, No.9, pp.675-692.
12.
Pan E., Bevis M., Han F., Zhou H. and Zhu R. (2007): Surface deformation due to loading of a layered elastic half-space: a rapid numerical kernel based on a circular loading element. – Geophys. J. Int., vol.171, pp.11-24.
13.
Ai Z.Y., Feng D.L. and Cang N.R. (2014): Analytical layer element solutions for deformations of transversely isotropic multilayered elastic media under nonaxisymmetric loading. – Int. J. Numer. Anal. Meth. Geomech., vol.38, pp.1585–1599.
14.
Zhang P., Lin G., Liu J. and Wang W. (2016): Response of multilayered transversely isotropic medium due to axisymmetric loads. – Int. J. Numer. Anal. Meth. Geomech., vol.40, pp.827–864.
15.
Ai Z.Y., Liu C.L. and Wang L.H. (2017): Transient response of a transversely isotropic multilayered half-space due to a vertical loading. – Applied Mathematical Modelling, vol.50, pp.414-431.
16.
Dziewonski A.M. and Anderson D.L. (1981): Preliminary reference earth model. – Phys. Earth Planet. Inter., vol.25, No.4, pp.297–356.
17.
Rundle J.B. (1982): Some solutions for static and pseudo-static deformation in layered, nonisothermal, porous media. – J. Phys. Earth, vol.30, pp.421-440.
18.
Small J.C. and Booker J.R. (1986): The behaviour of layered soil or rock containing a decaying heat source. – Int. J. Numer. Anal. Methods Geomech., vol.10, pp.501-519.
19.
Pan E. (1990): Thermoelastic deformation of a transversely isotropic and layered half-space by surface loads and internal sources. – Phys. Earth Planet. Inter., vol.60, pp.254-264.
20.
Ghosh M.K. and Kanoria M. (2007): Displacements and stresses in composite multi-layered media due to varying temperature and concentrated load. – Applied Mathematics and Mechanics (English Edition), vol.28, No.6, pp.811-822.
21.
Kolyano Y.M., Protsyuk B.V. and Sinyuta V.M. (1991): The axissymmetric static problem of thermoelasticity for a multilayered cylinder. – J. Appl. Maths. Mechs., vol.55, No.6, pp.920-926.
22.
Jane K.C. and Lee Z.Y. (1999): Thermoelasticity of multilayered cylinders. – Journal of Thermal Stresses, vol.22, pp.57-74.
23.
Lee Z.Y., Chen C.K. and Hung C.I. (2001): Transient thermal stress analysis of multilayered hollow cylinder. – Acta Mechanica, vol.151, pp.75-88.
24.
Lee Z.Y. (2004): Coupled problem of thermoelasticity for multilayered spheres with time dependent boundary conditions. – Journal of Marine Science and Technology, vol.12, No.2, pp.93-101.
25.
Ai Z.Y., Wang L.J. and Li B. (2015): Analysis of axisymmetric thermo-elastic problem in multilayered material with anisotropic thermal diffusivity. – Computers and Geotechnics, vol.65, pp.80–86.
26.
Ai Z.Y. and Wang L.J. (2015): Time-dependent analysis of 3D thermo-mechanical behaviour of a layered half-space with anisotropic thermal diffusivity. – Acta Mech., vol.226, No.9, pp.2939-2954.
27.
Ai Z.Y., Wang L.U. and Zeng K. (2015): Analytical layer-element method for 3D thermoelastic problem of layered medium around a heat source. – Meccanica, vol.50, pp.49-59.
28.
Wang L.J. and Ai Z.Y. (2015): Plane strain and three-dimensional analyses for thermo-mechanical behavior of multilayered transversely isotropic materials. – International Journal of Mechanical Sciences, vol.103, pp.199-211.
29.
Hou P.F., He S. and Chen C.P. (2011): 2D general solution and fundamental solution for orthotropic thermoelastic materials. – Engineering Analysis with Boundary Elements, vol.35, pp.56–60.
30.
Hou P.F., Jiang H.Y., Tong J. and Xiong S.M. (2014): Study on the coated isotropic thermoelastic material based on the three-dimensional Green’s function for a point heat source. – International Journal of Mechanical Sciences, vol.83, pp.155-162.
31.
Ai Z.Y. and Wang L.J. (2016): Three-dimensional thermo-hydro-mechanical responses of stratified saturated porothermoelastic material. – Applied Mathematical Modelling, vol.40, pp.8912-8933.
32.
Ai Z.Y., Wang Q.L. and Wang L.J. (2016): Axisymmetric coupled thermo-mechanical response of multilayered elastic medium. – Meccanica, vol.51, pp.1405–1417.
33.
Ai Z.Y., Zhao Z. and Wang L.J. (2017): Thermo-mechanical coupling response of a layered isotropic medium around a cylindrical heat source. – Computers and Geotechnics, vol.83, pp.159-167.
34.
Lu S., Liu J., Lin G. and Zhang P. (2017): Modified scaled boundary finite element analysis of 3D steady-state heat conduction in anisotropic layered media. – International Journal of Heat and Mass Transfer, vol.108, pp.2462–2471.
35.
Nowacki W. (1975): Dynamical Problems of Thermoelasticity. – Noordhoff, Leyden, The Netherlands.
36.
Vashisth A.K., Rani K. and Singh K. (2015): Quasi-static planar deformation in a medium composed of elastic and thermoelastic solid half spaces due to seismic sources in an elastic solid. – Acta Geophysica, vol.63, No.3, pp.605-633.
38.
Garg N.R. and Singh S.J. (1985): Residual response of a multilayered half-space to two-dimensional surface loads. – Bull. Ind. Soc. Earthq. Tech., vol.22, pp.39–52.
39.
Ahrens T.J. (1995): Mineral physics and crystallography: a Handbook of physical constants. – American Geophysical Union, Washington, D.C.
40.
Aki K. and Richards P.G. (1980): Quantitative Seismology: Theory and Methods, Volumes I and II. – W.H. Freeman and Company, San Francisco, U.S.A.
41.
Schapery R.A. (1962): Approximate methods of transform inversion for viscoelastic stress analysis. – Proc. 4th US Nat. Congr. Appl. Mech., vol.2, pp.1075–1085.
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