Mechanical and Thermal Stresses in a FGPM Hollow Cylinder Due to Non-Axisymmetric Loads

Subject Areas : Engineering

M Jabbari ¹ , M Meshkini ² , M.R Eslami ³

1 - South Tehran Branch, Islamic Azad University
2 - South Tehran Branch, Islamic Azad University
3 - Department of Mechanical Engineering, Amirkabir University of Technology

Received: 2010-12-25 Accepted : 2011-02-15 Published : 2011-03-30

Keywords: Hollow cylinder, FGPM, Non-Homogenous, Non-axisymmetric, Navier equations,

Abstract :

In this paper, the general solution of steady-state two-dimensional non-axisymmetric mechanical and thermal stresses and mechanical displacements of a hollow thick cylinder made of fluid-saturated functionally graded porous material (FGPM) is presented. The general form of thermal and mechanical boundary conditions is considered on the inside and outside surfaces. A direct method is used to solve the heat conduction equation and the non-homogenous system of partial differential Navier equations, using the Complex Fourier Series and the power law functions method. The material properties, except of Poisson's ratio, are assumed to depend on the radial variable r and they are expressed as power law functions.

References:

[1] Lutz M.P., Zimmerman R.W., 1996, Thermal stresses and effective thermal expansion coefficient of functionally graded sphere, Journal of Thermal Stresses 19:39-54.

[2] Zimmerman R.W., Lutz M.P., 1999, Thermal stresses and thermal expansion in a uniformly heated functionally graded cylinder, Journal of Thermal Stresses 22: 177-188.

[3] Jabbari M., Sohrabpour S., Eslami MR., 2003, General solution for mechanical and thermal stresses in functionally graded hollow cylinder due to radially symmetric loads, ASME Journal of Applied Mechanics 70: 111-118.

[4] Poultangari R., Jabbari M., Eslami M.R., 2008, Functionally graded hollow spheres under non-axisymmetric thermo-mechanical loads, International Journal of Pressure Vessels and Piping 85: 295-305.

[5] Shariyat M., Lavasani S.M.H., Khaghani M., 2009, 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.

[6] Lü C.F., Chen W.Q., Lim C.W., 2009, Elastic mechanical behavior of nano-scaled FGM films incorporating surface energies, Composites Science and Technology 69: 1124-1130.

[7] Afsar A.M., Sekine H., 2002, Inverse problems of material distributions for prescribed apparent fracture toughness in FGM coatings around acircular hole in infinite elastic media, Composites Science and Technology 62: 1063-1077.

[8] Zhang D.-G., Zhou Y.-H., 2008, A theoretical analysis of FGM thin plates based on physical neutral surface, Computational Materials Science 44: 716-720.

[9] Fazelzadeh S.A.., Hosseini M., 2007, Aerothermoelastic behavior of supersonic rotating thin-walled beams made of functionally graded materials, Journal of Fluids and Structures 23: 1251-1264.

[10] Ootao Y., Tanigawa Y., 2004, Transient thermoelastic problem of functionally graded thick strip due to non-uniform heat supply, Composite Structures 63(2): 139-146.

[11] Jabbari M., Sohrabpour S., Eslami M.R., 2002, 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.

[12] Farid M., Zahedinejad P., Malekzadeh P., 2010, Three-dimensional temperature dependent free vibration analysis of functionally graded material curved panels resting on two-parameter elastic foundation using a hybrid semi-analytic, differential quadrature method, Materials and Design 31: 2-13.

[13] Bagri A., Eslami M.R., 2008, Generalized coupled thermoelasticity of functionally graded annular disk considering the Lord–Shulman theory, Composite Structures 83: 168-179.

[14] Samsam Shariat B.A., Eslami M.R., 2007, Buckling of thick functionally graded plates under mechanical and thermal loads, Composite Structures 78: 433–439.

[15] Jabbari M., Bahtui A., Eslami MR., 2009, Axisymmetric mechanical and thermal stresses in thick short length functionally graded material cylinder, International Journal of Pressure Vessels and Piping 86: 296-306.

[16] Thieme M., Wieters K.-P., Bergner F., Scharnweber D., Worch H., Ndop J., Kim T.J., Grill., 1999, Titanium powder sintering for preparation of a porous FGM Destined as a skeletal replacement implant, Materials Science Forum 308-311: 374-382.

[17] Biot M.A., 1935, Le proble'me de la consolidation des matie'res argileuses sous une charge, Annales de la Societe Scientifique de Bruxelles B 55: 110-113.

[18] Biot M.A.., 1941, General theory of three-dimensional consolidation, Journal of Applied Physics 12: 155-164.

[19] De Boer R., 1996, Highlights in the historical development of the porous media theory: toward a consistent macroscopic theory, Applied Mechanics Reviews 49: 201-262.

[20] Detournay E., Cheng A.H.-D., 1993, Fundamentals of Poroelasticity, in: Comprehensive Rock Engineering: Principles, Practice and Projects, edited by J.A. Hudson, Pergamon, Oxford, 113-171.

[21] Sandhu R.S., Wilson E.L., 1969, Finite element analysis of seepage in elastic media, ASCE Journal of the Engineering Mechanics 95: 641-652.

[22] Detournay E., Cheng A.H.-D.,1993, Fundamentals of Poroelasticity, in: Comprehensive Rock Engineering: Principles, Practice and Projects, Chapter 5, vol. II, Analysis and Design Method, edited by C. Fairhurst, Pergamon Press, 113-171.

[23] Abousleiman Y., Ekboote S., 2005, solutions for inclined borehole in porothermoelastic transversely isotropic medium, ASME Journal of Applied Mechanics 72(2): 102-114.

[24] Chen P.Y.P., 1980, Axismmetric thermal stresses in an anisotropic finite hollow cylinder, Journal of Thermal Stresses 6(2-4): 197-205.

[25] Bai B., 2006, Fluctuation responses of saturated porous media subjected to cyclic thermal loading, Computers and Geotechnics 33: 396-403.

[26] Wang Y., Papamichos E., 1994, An analytical solution for conductive heat flow and the thermally induced fluid flow around a wellbore in a poroelastic medium, Water Resource Research 36(5): 3375-3384.

[27] Wang Y., Papamichos E., 1999, Thermal effects on fluid flow and hydraulic fracturing from wellbores and cavities in low-permeability formations, International Journal for Numerical and Analytical Methods in Geomechanics 23(15): 1819-1834

[28] Ghassemi A., Tao Q., 2009, Influence of coupled chemo-poro-thermoelastic processes on pore pressure and stress distributions around a wellbore in swelling shale, Journal of petroleum science and Engineering 67: 57-64

[29] Wirth B., Sobey I., 2006, An axisymmetric and fully 3D poroelastic model for the evolution of hydrocephalus, Mathematical Medicine and Biology 23:363-388.

[30] Yang D., Zhang Z., 2002, Poroelastic wave equation including the Biot/squirt mechanism and the solid/fluid coupling anisotropy, Wave Motion 35: 223-245

[31] Arora A., Tomar S.K., 2007, Elastic waves along a cylindrical borehole in a poroelastic medium saturated by two immiscible fluids, Journal of Earth System Science 116(3): 225-234.

[32] Hamiel Y., Lyakhovsky V., Agnon A., 2004, Coupled evolution of damage and porosity in poroelastic media: theory and applications to deformation of porous rocks, Geophysical Journal International 156: 701-713

[33] Ghassemi A., 2007, Stress and pore prepressure distribution around a pressurized, cooled crack in holw permeability rock, Proceedings of the Thirty-Second Workshop on Geothermal Reservoir Engineering, Stanford University, Stanford, California, January 22-24, SGP-TR-183

[34] Youssef H.M., 2007, Theory of generalized porothermoelasticity, International Journal of Rock Mechanics & Mining Sciences 44: 222-227.

[35] Jourine S., Valkoo P.P., Kronenberg A.K., 2004, Modelling poroelastic hollow cylinder experiments with realistic boundary conditions, International Journal for Numerical and Analytical Methods in Geomechanics 28: 1189-1205 (DOI: 10.1002/nag.383).