Stress Analysis in Thermosensitive Elliptical Plate with Simply Supported Edge and Impulsive Thermal Load

Document Type: Research Paper


1 M.G. College, Armori, Gadchiroli, India

2 Priyadarshini J. L., College of Engineering, Nagpur, India


The paper concerns the thermoelastic problems in a thermosensitive elliptical plate subjected to the activity of a heat source which changes its place on the plate surface with time. The solution of conductivity equation and the corresponding initial and boundary conditions is obtained by employing a new integral transform technique. In addition, the intensities of bending moments, resultant force, etc. are formulated involving the Mathieu and modified functions and their derivatives. The analytical solution for the thermal stress components is obtained in terms of resultant forces and resultant moments.


[1] Touloukian Y.S., 1970, Thermophysical Properties of Matter, Conductivity-Metallic Elements and Alloys, New York.
[2] Touloukian Y.S., 1973, Thermophysical Properties of Matter, Specific Heat-Metallic Elements and Alloys, New York.
[3] Touloukian Y.S., 1973, Thermophysical Properties of Matter, Thermal Diffusivity, New York.
[4] Touloukian Y.S., 1975, Thermophysical Properties of Matter, Thermal Expansion-Metallic Elements and Alloys, New York.
[5] Lee H.-J., 1998, The effect of temperature dependent material properties on the response of piezoelectric composite materials, Journal of Intelligent Material Systems and Structures 9(7): 503-508.
[6] Zhu X. K., Chao Y. U., 2002, Effect of temperature-dependent material properties on welding simulation, Computers & Structures 80(11): 967-976.
[7] Shariyat M., 2007, Thermal buckling analysis of rectangular composite plates with temperature dependent properties based on a layer wise theory, Thin-Walled Structures 45(4): 439-452.
[8] Sugano Y., 1983, Analysis of transient thermal stresses in an orthotropic finite rectangular plate exhibiting temperature-dependent material properties, Nippon Kikai Gakkai Ronbunshu 49: 1315-1323.
[9] Sugano Y., Maekawa T., 1985, Transient thermal stresses in a perforated plate of variable thickness exhibiting temperature-dependent material properties, Nippon Kikai Gakkai Ronbunshu 51: 63-71.
[10] Noda N., 1986, Thermal Stresses in Materials with Temperature-Dependent Properties, North-Holland, Amsterdam.
[11] Noda N., Daichyo Y., 1987, Transient thermoelastic problem in a long circular cylinder with temperature dependent properties, Transactions of the Japan Society of Mechanical Engineers Series A 53(487): 559-565.
[12] Noda N., 1991, Thermal stresses in materials with temperature-dependent properties, American Society of Mechanical Engineers 44(9): 383-397.
[13] Tang S., 1968, Thermal stresses in temperature-dependent isotropic plates, Journal of Spacecraft and Rockets 5(8): 987-990.
[14] Tang S., 1969, Some problems in thermoelasticity with temperature-dependent properties, Journal of Spacecraft and Rockets 6(2): 217-219.
[15] Tanigawa Y., Akai T., Kawamura R., Oka N., 1996, Transient heat conduction and thermal stress problems of a nonhomogeneous plate with temperature-dependent material properties, Journal of Thermal Stresses 19(1): 77-102.
[16] Popovych V. S., Harmatiy H. Y., 1993, Analytical and numerical methods of solutions of heat conduction problems with temperature-sensitive body convective heat transfer, Pidstryhach Institute for Applied Problems of Mechanics and Mathematics 1993(3): 67-93.
[17] Harmatiy H. Y., Kutniv M. B., Popovich V. S., 2002, Numerical solution of unsteady heat conduction problems with temperature-sensitive body convective heat transfer, Engineering 2002(1): 21-25.
[18] Rakocha I., Popovych V., 2016, The mathematical modeling and investigation of the stress-strain state of the three-layer thermosensitive hollow cylinder, Acta Mechanica et Automatica 10(3): 181-188.
[19] Kushnir R. M., Protsiuk Y. B., 2010, Thermoelastic state of layered thermosensitive bodies of revolution for the quadratic dependence of the heat-conduction coefficients, Materials Science 46(1): 1-15.
[20] Yevtuchenko A. A., Kuciej M., Och E., 2014, Influence of thermal sensitivity of the pad and disk materials on the temperature during braking, International Communications in Heat and Mass Transfer 55: 84-92.
[21] Kushnir R. M., Popovych V., 2006, Stressed state thermosensitive body rotation in the plane axialsymmetric temperature field, Median Mechanics 2006(2): 91-96.
[22] Kushnir R. M., Popovych V. S., 2011, Heat Conduction Problems of Thermosensitive Solids under Complex Heat Exchange, Heat Conduction-Basic Research.
[23] Harmatij H., Król M., Popovycz V., 2013, Quasi-static problem of thermoelasticity for thermosensitive infinite circular cylinder of complex heat exchange, Advances in Pure Mathematics 3(4): 430-437.
[24] Bhad P., Varghese V., Khalsa L.H., 2016, Heat source problem of thermoelasticity in an elliptic plate with thermal bending moments, Journal of Thermal Stresses 40(1): 96-107.
[25] Bhad P., Khalsa L., Varghese V., 2016, Transient thermoelastic problem in a confocal elliptical disc with internal heat sources, Advances in Mathematical Sciences and Applications 25: 43-61.
[26] Bhad P., Khalsa L., Varghese V., 2016, Thermoelastic theories on elliptical profile objects: an overview & prospective, International Journal of Advances in Applied Mathematics and Mechanics 4(2): 12-20.
[27] Bhad P., Khalsa L., Varghese V., 2016, Thermoelastic-induced vibrations on an elliptical disk with internal heat sources, Journal of Thermal Stresses 40(4): 502-516.
[28] Bhad P., Varghese V., Khalsa L., 2016, A modified approach for the thermoelastic large deflection in the elliptical plate, Archive of Applied Mechanics 87(4): 767-781.
[29] Gupta R.K., 1964, A finite transform involving Mathieu functions and its application, The Proceedings of the National Academy of Sciences Part A, India.
[30] Pateriya M.P., 1975, Internal heat generation in an infinite plate with a transverse circular cylindrical hole, Indian Journal of Pure and Applied Mathematics 8(11): 1340-1346.
[31] McLachlan N.W., 1947, Theory and Application of Mathieu Function, Clarendon Press, Oxford.
[32] Varghese V., Khobragade N.W., 2007, Alternative solution of transient heat conduction in a circular plate with radiation, International Journal of Applied Mathematics 20(8): 1133-1140.