Thermoelastic Analysis of a Rectangular Plate with Nonhomogeneous Material Properties and Internal Heat Source

Subject Areas : Engineering

V. R Manthena ¹ , N.K Lamba ² , G.D Kedar ³

1 - Department of Mathematics, RTM Nagpur University, Nagpur, India
2 - Department of Mathematics, Shri Lemdeo Patil Mahavidyalaya, Nagpur, India
3 - Department of Mathematics, RTM Nagpur University, Nagpur, India

Received: 2018-01-09 Accepted : 2018-03-06 Published : 2018-03-01

Keywords:

References:

[1] Al-Hajri M., Kalla S.L., 2004, On an integral transform involving Bessel functions, Proceedings of the International Conference on Mathematics and its Applications.

[2] Birkoff G., Rota G. C., 1989, Ordinary Differential Equations, Wiley, New York.

[3] Churchill R.V., 1972, Operational Mathematics, Mc-Graw Hill.

[4] Ding S.H., Li X., 2015, Thermoelastic analysis of nonhomogeneous structural materials with an interface crack under uniform heat flow, Applied Mathematics and Computation Archive 271: 22-33.

[5] Edited by the Japan Society of Mechanical Engineers, 1980, Elastic Coefficient of Metallic Materials, Japan Society of Mechanical Engineers.

[6] Gupta A.K., Singhal P., 2010, Thermal effect on free vibration of non-homogeneous orthotropic visco-elastic rectangular plate of parabolically varying thickness, Applied Mathematics 1: 456-463.

[7] Gupta A.K., Saini M., Singh S., Kumar R., 2014, Forced vibrations of non-homogeneous rectangular plate of linearly varying thickness, Journal of Vibration Control 20: 876-884.

[8] Hata T., 1983, Thermal stresses in a nonhomogeneous thick plate with surface radiation under steady distribution of temperature, The Japan Society of Mechanical Engineers 49: 1515-1521.

[9] Kassir M.K., 1972, Boussinesq problems for nonhomogeneous solid, Proceedings of the American Society of Civil Engineers,Journal of the Engineering Mechanics Division 98: 457-470.

[10] Kawamura R., Huang D., Tanigawa Y., 2001, Thermoelastic deformation and stress analyses of an orthotropic nonhomogeneous rectangular plate, Proceedings of the Fourth International Congress on Thermal Stresses.

[11] Kumar Y., 2012, Free vibrations of simply supported nonhomogeneous isotropic rectangular plates of bilinearly varying thickness and elastically restrained edges against rotation using Rayleigh-Ritz method, Earthquake Engineering and Engineering Vibration 11: 273-280.

[12] Lal R., Kumar Y., 2013, Transverse vibrations of nonhomogeneous rectangular plates with variable thickness, Mechanics of Advanced Materials and Structures 20: 264-275.

[13] Manthena V.R., Lamba N.K., Kedar G.D., 2016, Transient thermoelastic problem of a nonhomogeneous rectangular plate, Journal of Thermal Stresses 40: 627-640.

[14] Martynyak R.M., Dmytriv M.I., 2010, Finite-element investigation of the stress-strain state of an inhomogeneous rectangular plate, Journal of Mathematical Sciences 168: 633-642.

[15] Morishita H., Tanigawa Y., 1998, Formulation of three dimensional elastic problem for nonhomogeneous medium and its analytical development for semi-infinite body, The Japan Society of Mechanical Engineers 97: 97-104.

[16] Muravskii G.B., 2008, Response of an elastic half-space with power-law nonhomogeneity to static loads, Archive of Applied Mechanics 78: 965.

[17] Pandita B.B., Kulkarni V.S., 2015, Finite difference approach for nonhomogeneous problem of thermal stresses in cartesian domain, International Journal of Advances in Applied Mathematics and Mechanics 3: 100-112.

[18] Sharma S., Gupta U.S., Singhal P., 2012, Vibration analysis of nonhomogeneous orthotropic rectangular plates of variable thickness resting on winkler foundation, Journal of Applied Science and Engineering 15: 291-300.

[19] Sugano Y., 1987, Transient thermal stresses in a nonhomogeneous doubly connected region, The Japan Society of Mechanical Engineers 53: 941-946.

[20] Tanigawa Y., Ootao Y., Kawamura R., 1991, Thermal bending of laminated composite rectangular plates and nonhomogeneous plates due to partial heating, Journal of Thermal Stresses 14: 285-308.

[21] Tanigawa Y., 1995, Some basic thermoelastic problems for nonhomogeneous structural materials, Applied Mechanics Reviews 48: 287-300.

[22] Tanigawa Y., Kawamura R., Ishida S., 2002, Derivation of fundamental equation systems of plane isothermal and thermoelastic problems for in-homogeneous solids and its applications to semi-infinite body and slab, Theoretical and Applied Mechanics 51: 267-279.

[23] Tokovyy Y., Ma C-C., 2009, Analytical solutions to the 2D elasticity and thermoelasticity problems for inhomogeneous planes and half-planes, Archive of Applied Mechanics 79: 441-456.

[24] Wang C.Y., Wang C.M., 2011, Exact solutions for vibrating nonhomogeneous rectangular membranes with exponential density distribution, The IES Journal Part A: Civil & Structural Engineering 4: 37-40.

[25] Yang Q., Zheng B., Zhang K., Zhu J., 2013, Analytical solution of a bilayer functionally graded cantilever beam with concentrated loads, Archive of Applied Mechanics 83: 455-466.