A Rapidly Convergent Nonlinear Transfinite Element Procedure for Transient Thermoelastic Analysis of Temperature-Dependent Functionally Graded Cylinders
Subject Areas : Engineering
M Shariyat
1
(Faculty of Mechanical Engineering, K.N.T. University of Technology)
Keywords: Nonlinear transfinite element, Transient thermoelastic analysis, Enhanced convergence, Functionally graded cylinders, Temperature-dependency,
Abstract :
In the present paper, the nonlinear transfinite element procedure recently published by the author is improved by introducing an enhanced convergence criterion to significantly reduce the computational run-times. It is known that transformation techniques have been developed mainly for linear systems, only. Due to using a huge number of time steps, employing the conventional time integration methods requires quite huge computational time and leads to remarkable error accumulation, numerical instability, or numerical damping, especially for long investigation times. The present method specially may be extended to problems where the required time steps are of the order of the round-off errors (e.g., coupled thermoelasticty problems). The present procedure is employed for transient thermoelastic analysis of thick-walled functionally graded cylinders with temperature-dependent material properties, as an example. To reduce the effect of the artificial local heat and stress shock source generation at the mutual boundaries of the elements, second order elements are used. Influences of various parameters on the temperature and stress distributions are investigated. Furthermore, results of the proposed transfinite element technique are compared with the results obtained by other references to verify the validity, accuracy, and efficiency of the proposed method.
[1] Noda N., 1991, Thermal stresses in materials with temperature-dependent properties, ASME Applied Mechanics Review 44: 83-97.
[2] Tanigawa Y., 1995, Some basic thermoelastic problems for non-homogeneous structural materials, ASME Applied Mechanics Review 48: 287-300.
[3] Zimmerman R.W., Lutz M.P., 1999, Thermal stress and thermal expansion in a uniformly heated functionally graded cylinder, Journal of Thermal Stresses 22: 88-177.
[4] Obata Y., Noda N., 1994, Steady thermal stresses in a hollow circular cylinder and a hollow sphere of a functionally gradient material, Journal of Thermal Stresses 17: 471-487.
[5] El-abbasi N., Meguid S.A., 2000, Finite element modeling of the thermoelastic behavior of functionally graded plates and shells, International Journal of Computational Engineering Science 1: 51-165.
[6] Jabbari M., Sohrabpour, S. Eslami M.R., 2001, Mechanical and thermal stresses in a functionally graded hollow cylinder due to radially symmetric loads, International Journal of Pressure Vessels and Piping 79: 493-497.
[7] Liew K.M., Kitipornchai S., Zhang X.Z., Lim C.W., 2003, Analysis of the thermal stress behavior of functionally graded hollow circular cylinders, International Journal of Solids and Structures 40: 2355-2380.
[8] Jabbari M., Sohrabpour S., Eslami M.R., 2003, General solution for mechanical and thermal stresses in a functionally graded hollow cylinder due to nonaxisymmetric steady-state loads. ASME Journal of Applied Mechanics 70: 111-118.
[9] Ching H.K., Yen S.C., 2005, Meshless local Petrov-Galerkin analysis for 2D functionally graded elastic solids under mechanical and thermal loads, Composites Part B: Engineering 36: 223-240.
[10] Wang X., 1995, Thermal shock in a hollow cylinder caused by rapid arbitrary heating, Journal of Sound and Vibration 183(5): 899-906.
[11] Kandil A., EL-Kady A.A., EL-Kafrawy A., 1995, Transient thermal stress analysis of thick-walled cylinders, International Journal of Mechanical Sciences37: 721-732.
[12] Segall A.E., 2003, Transient analysis of thick-walled piping under polynomial thermal loading, Nuclear Engineering and Design 226: 183-191.
[13] Segall A.E., 2004, Thermoelastic stresses in an axisymmetric thick-walled tube under an arbitrary internal transient, ASME Journal of Pressure Vessel Technology 126: 327-332.
[14] Lee Z.Y., 2005, Hybrid numerical method applied to 3-D multilayered hollow cylinder with periodic loading conditions, Applied Mathematics and Computation 166: 95-117.
[15] Shahani A.R., Nabavi S.M., 2007, Analytical solution of the quasi-static thermoelasticity problem in a pressurized thick-walled cylinder subjected to transient thermal loading, Applied Mathematical Modelling 31:1807-1818.
[16] Ramadan K., 2009, Semi-analytical solutions for the dual phase lag heat conduction in multilayered media, International Journal of Thermal Sciences 48(1): 14-25.
[17] Reddy J.N., Chin C.D., 1998, Thermomechanical analysis of functionally graded cylinders and plates, Journal of Thermal Stresses 21: 593-626.
[18] Praveen G.N., Chin C.D., Reddy J.N., 1999, Thermoelastic analysis of a functionally graded ceramic-metal cylinder, ASCE Journal of Engineering Mechanics 125(11): 1259-1267.
[19] Obata Y., Kanayama K., Ohji T., Noda N., 1999, Two-dimensional unsteady thermal stresses in a partially heated circular cylinder made of functionally gradient materials, in: 3rd International Congress on Thermal Stresses, 595-598.
[20] Awaji H., Sivakumar R., 2001, Temperature and stress distribution in a hollow cylinder of functionally graded material: the case of temperature-independent material properties, Journal of the American Ceramic Society 84: 1059-1065.
[21] Kim K.S., Noda N., 2002, Green’s function approach to unsteady thermal stresses in an infinite hollow cylinder of functionally graded material, Acta Mechanica 156: 145-61.
[22] Sladek J., Sladek V., Zhang C., 2003, Transient heat conduction analysis in functionally graded materials by the meshless local boundary integral equation method, Computational Materials Science 28: 494-504.
[23] Wang B.L., Mai Y.W., Zhang X.H., 2004, Thermal shock resistance of functionally graded materials, Acta Materialia 52: 4961-4972.
[24] Wang B.L., Mai Y.W., 2005, Transient one-dimensional heat conduction problems solved by finite element, International Journal of Mechanical Sciences 47: 303-317.
[25] Hosseini S.M., Akhlaghi M., Shakeri M., 2007, Transient heat conduction in functionally graded thick hollow cylinders by analytical method, Heat and Mass Transfer 43: 669-675.
[26] Shao Z.S., Wang T.J., Ang K.K., 2007, Transient thermo-mechanical analysis of functionally graded hollow circular cylinders, Journal of Thermal Stresses 30(1): 81-104.
[27] Shao Z.S., Ma G.W., 2008, Thermo-mechanical stresses in functionally graded circular hollow cylinder with linearly increasing boundary temperature, Composite Structures 83(3): 259-265.
[28] Hosseini S.M., 2009, Coupled thermoelasticity and second sound in finite length functionally graded thick hollow cylinders (without energy dissipation), Materials & Design 30( 6): 2011-2023.
[29] Shariyat M., 2008, Dynamic thermal buckling of suddenly heated temperature-dependent FGM cylindrical shells, under combined axial compression and external pressure, International Journal of Solids and Structures 45: 2598-2612.
[30] He T., Tian X., Shen Y., 2002, Two-dimensional generalized thermal shock problem of a thick piezoelectric plate of infinite extent, International Journal of Engineering Science 40: 2249-2264.
[31] Tian X., Shen Y., Chen C., He T., 2006, A direct finite element method study of generalized thermoelastic problems, International Journal of Solids and Structures 43: 2050-2063.
[32] Bagri A., Eslami M.R., 2008, Generalized coupled thermoelasticity of functionally graded annular disk considering the Lord–Shulman theory, Composite Structures 83(2): 168-179.
[33] Shakeri M., Akhlaghi M., Hoseini S.M., 2006, Vibration and radial wave propagation velocity in functionally graded thick hollow cylinder, Composite Structures 76: 174-181.
[34] Shariyat M., Eslami M.R., 1996, Isoparametric finite-element thermoelasto-plastic creep analysis of shells of revolution, International Journal of Pressure Vessels and Piping 68(3): 249-259.
[35] Zienkiewicz O.C., Taylor R.L., 2005, The Finite Element Method: Its Basis and Fundamentals, Butterworth-Heinemann, 6th edition.
[36] Reddy J.N., 2005, An Introduction to the Finite Element Method, McGraw-Hill, 3rd edition.
[37] Heinrich J.C., Pepper D.W., 2005, The Finite Element Method: Basic Concepts and Applications, Taylor & Francis, 2nd edition.
[38] Shariyat M., 2009, A nonlinear Hermitian transfinite element method for transient behavior analysis of hollow functionally graded cylinders with temperature-dependent materials under thermo-mechanical loads, International Journal of Pressure Vessels and Piping 86: 280-289.
[39] Shariyat M., Lavasani S.M.H., Khaghani M., 2010, Nonlinear transient thermal stress and elastic wave propagation analyses of thick temperature-dependent FGM cylinders, using a second-order point-collocation method, Applied Mathematical Modelling, doi: 10.1016/j.apm.2009.07.007.
[40] Shariyat M., Khaghani M., Lavasani S.M.H., 2010, Nonlinear thermoelasticity, vibration, and stress wave propagation analyses of thick FGM cylinders with temperature-dependent material properties, European Journal of Mechanics-A/Solids, doi: doi:10.1016/j.euromechsol.2009.10.007.
[41] Azadi M., Shariyat M., 2009, Nonlinear transient transfinite element thermal analysis of thick-walled FGM cylinders with temperature-dependent material properties. Meccanica, doi: 10.1007/s11012-009-9249-4.
[42] Shen H.-S., 2009, Functionally Graded Materials: Nonlinear Analysis of Plates and Shell, CRC Press, Taylor & Francis Group, Boca Raton.
[43] Touloukian Y.S., 1976, Thermophysical Properties of High Temperature Solid Materials, McMillan, New York.
[44] Hetnarski R.B., Eslami M.R., 2009, Thermal Stresses - Advanced Theory and Applications, Springer.
[45] Reddy, J.N., 2005, An Introduction to the Finite Element Method, 3rd edition, McGraw-Hill.
[46] Honig G., Hirdes U., 1984, A method for the numerical inversion of Laplace transforms, Journal of Computational and Applied Mathematics 10: 113-132.