Generalized thermoelastic functionally graded orthotropic hollow sphere under thermal shock with three-phase-lag effect |
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| Authors: | Avijit Kar M Kanoria |
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| Institution: | 1. Department of Mathematics, St. Xavier''s College 30, Park Street, Kolkata, 700 016, India;2. Department of Applied Mathematics, University of Calcutta, 92, A.P.C. Road, Kolkata, 700 009, India;1. Department of Mathematics, Faculty of Science, Zagazig University, P.O. Box 44519, Zagazig, Egypt;2. Department of Mathematics, Faculty of Science, Taif University, 888, Taif City, Saudi Arabia;3. Department of Mathematics, Transilvania University of Brasov, Romania;1. Faculty of Engineering, Shahrekord University, Shahrekord, Iran;2. The Academy of Sciences, Mechanical Engineering Department, Amirkabir University of Technology, Tehran, Iran;1. Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia;2. Department of Mathematics, Faculty of Science, Kafrelsheikh University, Kafrelsheikh 33516, Egypt;1. Department of Mathematics and Natural Sciences, Gulf University for Science and Technology, P.O. Box 7207, Hawally 32093, Kuwait;2. Texas A&M University, Mechanical Engineering Program, Engineering Building, P.O. Box 23874, Education City, Doha, Qatar;3. Applied Mechanics and Systems Research Laboratory, Tunisia Polytechnic School, University of Carthage, BP 743, 2048 La Marsa, Tunisia |
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| Abstract: | This problem deals with the determination of thermo-elastic interaction due to step input of temperature on the boundaries of a functionally graded orthotropic hollow sphere in the context of linear theories of generalized thermo-elasticity. Using the Laplace transformation the fundamental equations have been expressed in the form of vector–matrix differential equation which is then solved by eigenvalue approach. The inverse of the transformed solution is carried out by applying a method of Bellman et al. Stresses, displacement and temperature distributions have been computed numerically and presented graphically in a number of figures. A comparison of the results for different theories (TEWOED(GN-II), TEWED(GN-III) and three-phase-lag model) is presented. When the material is homogeneous, isotropic and outer radius of the hollow sphere tends to infinity, the corresponding results agree with that of existing literature for GN-III model. |
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