Nonlinear transient thermal stress and elastic wave propagation analyses of thick temperature-dependent FGM cylinders, using a second-order point-collocation method. (English) Zbl 1185.74011

Summary: Nonlinear transient thermal stress and elastic wave propagation analyses are developed for hollow thick temperature-dependent FGM cylinders subjected to dynamic thermomechanical loads. Stress wave propagation, wave shape distortion, and speed variation under impulsive mechanical loads in thermal environments are also investigated. In contrast to researches accomplished so far, a second-order formulation rather than a first-order one is employed to improve the accuracy. The FDM method (as a point-collocation FEM method) is used. It is known that other FEM methods cannot show the actual trend jumps due to distributing the abrupt changes in the quantities as the numerical errors and the residuals of the governing equations among the nodal results. Furthermore, the required computational time and allocated computer memory are much reduced by the present solution algorithm. The cylinder is not divided into isotropic sub-cylinders. Therefore, artificial wave reflections from the hard interfaces are avoided. Time variations of the temperatures, displacements, and stresses due to the dynamic or impulsive loads are determined by solving the resulted highly nonlinear governing equations using an iterative updating solution scheme. A sensitivity analysis includes effects of the volume fraction indices, dimensions, and temperature-dependency of the material properties is performed. Results reveal the significant effect of the temperature-dependency of the material properties on the thermoelastic stresses and present some interesting characteristics of the thermoelastic and wave propagation behaviors.


74F05 Thermal effects in solid mechanics
65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
74S20 Finite difference methods applied to problems in solid mechanics
Full Text: DOI


[1] Noda, N., Thermal stresses in materials with temperature-dependent properties, Appl. mech. rev., 44, 83-97, (1991)
[2] Tanigawa, Y., Some basic thermoelastic problems for non-homogeneous structural materials, Appl. mech. rev., 48, 287-300, (1995)
[3] Zimmerman, R.W.; Lutz, M.P., Thermal stress and thermal expansion in a uniformly heated functionally graded cylinder, J. therm. stresses, 22, 88-177, (1999)
[4] Obata, Y.; Noda, N., Steady thermal stresses in a hollow circular cylinder and a hollow sphere of a functionally gradient material, J. therm. stresses, 17, 471-487, (1994)
[5] El-abbasi, N.; Meguid, S.A., Finite element modeling of the thermoelastic behavior of functionally graded plates and shells, Int. J. comput. eng. sci., 1, 51-165, (2000)
[6] Jabbari, M.; Sohrabpour, S.; Eslami, M.R., Mechanical and thermal stresses in a functionally graded hollow cylinder due to radially symmetric loads, Int. J. press. vess. pip., 79, 493-497, (2002)
[7] Jabbari, M.; Sohrabpour, S.; Eslami, M.R., General solution for mechanical and thermal stresses in a functionally graded hollow cylinder due to nonaxisymmetric steady-state loads, ASME J. appl. mech., 70, 111-118, (2003) · Zbl 1110.74495
[8] Liew, K.M.; Kitipornchai, S.; Zhang, X.Z.; Lim, C.W., Analysis of the thermal stress behavior of functionally graded hollow circular cylinders, Int. J. solids struct., 40, 2355-2380, (2003) · Zbl 1087.74529
[9] Shen, H.S., Thermal postbuckling behavior of functionally graded cylindrical shells with temperature-dependent properties, Int. J. solids struct., 41, 1961-1974, (2004) · Zbl 1106.74352
[10] Wang, X., Thermal shock in a hollow cylinder caused by rapid arbitrary heating, J. sound vib., 183, 5, 899-906, (1995) · Zbl 0982.74504
[11] Shahani, A.R.; Nabavi, S.M., Analytical solution of the quasi-static thermoelasticity problem in a pressurized thick-walled cylinder subjected to transient thermal loading, Appl. math. model., 31, 1807-1818, (2007) · Zbl 1167.74392
[12] Ramadan, K., Semi-analytical solutions for the dual phase lag heat conduction in multilayered media, Int. J. therm. sci., (2008)
[13] Kandil, A.; EL-Kady, A.A.; EL-Kafrawy, A., Transient thermal stress analysis of thick-walled cylinders, Int. J. mech. sci., 37, 721-732, (1995) · Zbl 0832.73011
[14] Segall, A.E., Transient analysis of thick-walled piping under polynomial thermal loading, Nucl. eng. des., 226, 183-191, (2003)
[15] Segall, A.E., Thermoelastic stresses in an axisymmetric thick-walled tube under an arbitrary internal transient, ASME J. press. vess. technol., 126, 327-332, (2004)
[16] Lee, Z.Y., Hybrid numerical method applied to 3-D multilayered hollow cylinder with periodic loading conditions, Appl. math. comput., 166, 95-117, (2005) · Zbl 1079.74668
[17] Reddy, J.N.; Chin, C.D., Thermomechanical analysis of functionally graded cylinders and plates, J. therm. stresses, 21, 593-626, (1998)
[18] Praveen, G.N.; Chin, C.D.; Reddy, J.N., Thermoelastic analysis of a functionally graded ceramic – metal cylinder, ASCE J. eng. mech., 125, 11, 1259-1267, (1999)
[19] Y. Obata, K. Kanayama, T. Ohji, N. Noda, Two-dimensional unsteady thermal stresses in a partially heated circular cylinder made of functionally gradient materials, in: Third International Congress on Thermal Stresses, 1999, pp. 595-598.
[20] Awaji, H.; Sivakumar, R., Temperature and stress distribution in a hollow cylinder of functionally graded material: the case of temperature-independent material properties, J. am. ceram. soc., 84, 1059-1065, (2001)
[21] Kim, K.S.; Noda, N., Green’s function approach to unsteady thermal stresses in an infinite hollow cylinder of functionally graded material, Acta mech., 156, 145-161, (2002) · Zbl 1068.74017
[22] Sladek, J.; Sladek, V.; Zhang, C., Transient heat conduction analysis in functionally graded materials by the meshless local boundary integral equation method, Comput. mater. sci., 28, 494-504, (2003)
[23] Wang, B.L.; Mai, Y.W.; Zhang, X.H., Thermal shock resistance of functionally graded materials, Acta mater., 52, 4961-4972, (2004)
[24] Wang, B.L.; Mai, Y.W., Transient one-dimensional heat conduction problems solved by finite element, Int. J. mech. sci., 47, 303-317, (2005) · Zbl 1192.74094
[25] Hosseini, S.M.; Akhlaghi, M.; Shakeri, M., Transient heat conduction in functionally graded thick hollow cylinders by analytical method, Heat mass trans., 43, 669-675, (2007)
[26] Shao, Z.S.; Wang, T.J.; Ang, K.K., Transient thermo-mechanical analysis of functionally graded hollow circular cylinders, J. therm. stresses, 30, 1, 81-104, (2007)
[27] Shao, Z.S.; Ma, G.W., Thermo-mechanical stresses in functionally graded circular hollow cylinder with linearly increasing boundary temperature, Compos. struct., 83, 259-265, (2008)
[28] Shariyat, M., Dynamic thermal buckling of suddenly heated temperature-dependent FGM cylindrical shells, under combined axial compression and external pressure, Int. J. solids struct., 45, 2598-2612, (2008) · Zbl 1169.74438
[29] Heyliger, P.; Jilania, A., The free vibration of inhomogeneous elastic cylinders and spheres, Int. J. solids struct., 29, 2689-2708, (1992) · Zbl 0775.73140
[30] Steinberg, L., Inverse spectral problems for inhomogeneous elastic cylinders, J. elasticity, 38, 133-151, (1995) · Zbl 0828.73025
[31] Han, H.; Liu, G.R.; Xi, Z.C.; Lam, K.Y., Transient waves in a functionally graded cylinder, Int. J. solids struct., 38, 3021-3037, (2001) · Zbl 0977.74035
[32] El-Raheb, M., Transient waves in an inhomogeneous hollow infinite cylinder, Int. J. solids struct., 42, 5356-5376, (2005) · Zbl 1119.74438
[33] Shakeri, M.; Akhlaghi, M.; Hoseini, S.M., Vibration and radial wave propagation velocity in functionally graded thick hollow cylinder, Compos. struct., 76, 174-181, (2006)
[34] Ponnusamy, P., Wave propagation in a generalized thermoelastic solid cylinder of arbitrary cross-section, Int. J. solids struct., 44, 5336-5348, (2007) · Zbl 1242.74039
[35] Wang, X.; Dong, K., Magnetothermodynamic stress and perturbation of magnetic field vector in a non-homogeneous thermoelastic cylinder, Eur. J. mech. A-solid, 25, 98-109, (2006) · Zbl 1083.74019
[36] Dong, K.; Wang, X., Wave propagation characteristics in piezoelectric cylindrical laminated shells under large deformation, Compos. struct., 77, 171-181, (2007)
[37] Wang, X.; Sheng, G.G., Thermal vibration, buckling and dynamic stability of functionally graded cylindrical shells embedded in an elastic medium, J. reinf. plast. compo., 27, 117-134, (2008)
[38] Sheng, G.G.; Wang, X., Thermomechanical vibration analysis of a functionally graded shell with flowing fluid, Eur. J. mech. A-solid, 27, 1075-1087, (2008) · Zbl 1151.74364
[39] He, T.; Tian, X.; Shen, Y., Two-dimensional generalized thermal shock problem of a thick piezoelectric plate of infinite extent, Int. J. eng. sci., 40, 2249-2264, (2002) · Zbl 1211.74083
[40] Tian, X.; Shen, Y.; Chen, C.; He, T., A direct finite element method study of generalized thermoelastic problems, Int. J. solids struct., 43, 2050-2063, (2006) · Zbl 1121.74477
[41] Bagri, A.; Eslami, M.R., Generalized coupled thermoelasticity of functionally graded annular disk considering the lord – shulman theory, Compos. struct., (2007)
[42] H. Santos, C.M. Mota Soares, C.A. Mota Soares, J.N. Reddy, A semi-analytical finite element model for the analysis of cylindrical shells made of functionally graded materials under thermal shock, Compos. Struct. doi:10.1016/j.compstruct.2008.03.004. · Zbl 1227.74082
[43] Shariyat, M.; Eslami, M.R., Isoparametric finite-element thermoelasto-plastic creep analysis of shells of revolution, Int. J. press. vess. pip., 68, 3, 249-259, (1996)
[44] Huges, T.J.R., The finite element method: linear static and dynamic finite element analysis, (2000), Dover Publications
[45] Reddy, J.N., An introduction to the finite element method, (2005), McGraw-Hill · Zbl 0561.65079
[46] Bruck, H.A., A one-dimensional model for designing functionally graded materials to manage stress waves, Int. J. solids struct., 37, 6383-6395, (2000) · Zbl 0996.74045
[47] Samadhiya, R.; Mukherjee, A.; Schmauder, S., Characterization of discretely graded materials using acoustic wave propagation, Comput. mater. sci., 37, 20-28, (2006)
[48] Chung, T.J., Computational fluid dynamics, (2002), Cambridge University Press · Zbl 1037.76001
[49] Touloukian, Y.S., Thermophysical properties of high temperature solid materials, (1976), McMillan New York
[50] Noda, N., Thermal stresses, (2002), Taylor and Francis · Zbl 1068.74017
[51] Gerald, C.F.; Wheatley, P.O., Applied numerical analysis, (2003), Addison-Wesley
[52] Bathe, K.J., Finite element procedures, (2007), Prentice Hall Englewood Cliffs, New Jersey · Zbl 0511.73065
[53] Shariyat, M., Vibration and dynamic buckling control of imperfect piezoelectric FGM plates with temperature-dependent materials subjected to a thermo-electro-mechanical loading, Compos. struct., 88, 240-252, (2009)
[54] Shariyat, M., Dynamic buckling of imperfect laminated plates with piezoelectric sensors and actuators subjected to thermo-electro-mechanical loadings, considering the temperature-dependency of the material properties, Compos. struct., 88, 228-239, (2009)
[55] Shariyat, M., Dynamic buckling of suddenly loaded imperfect hybrid FGM cylindrical shells with temperature-dependent material properties under thermo-electro-mechanical loads, Int. J. mech. sci., 50, 1561-1571, (2008)
[56] Shariyat, M., A nonlinear Hermitian transfinite element method for transient behavior analysis of hollow temperature-dependent FGM cylinders under thermo-mechanical loads, Int. J. press. vess. pip., 86, 280-289, (2009)
[57] Chandrupatla, T.R.; Belegundu, A.D., Introduction to finite elements in engineering, (2002), Prentice Hall
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.