Analysis of Functionally Graded Cylindrical Vessels under Mechanical and Thermal Loads

Document Type : Research Article

Authors

Abstract

In this paper, a static analysis of functionally graded cylinders under axisymmetric mechanical and thermal loads is presented. It is assumed that the distribution of material properties through the thickness of the cylinder is continuous and graded according to a power low distribution. For solving equations, two-dimensional finite element method is employed. To this end, a functionally graded material element is defined for accurate finite element modeling of cylinder with continuous distribution of material properties and avoiding the limitation in the radius to thickness ratio. Numerical results are obtained for a clamped cylinder subjected to a uniform internal pressure and a simply supported cylinder subjected to a temperature distribution through the thickness. In addition, the numerical results for thick and thin cylinders are obtained. The results show that the stress and temperature distribution in functionally graded cylindrical shells are dependent on the material kind and distribution of material properties and this dependency can be utilized for controlling the stress level.

Keywords


[1] Tutuncu, N.; Ozturk, M.; "Exact Solutions for Stresses in Functionally Graded Pressure Vessels",Composites: Part B, p.p. 683-686, 2001.
[2] Horgan, C.O.; Chan, A.M.; "The Pressurized Hollow Cylinder or Disk Problem for Functionally Gradedm Isotropic Linearly Elastic Materials", Journal of Elasticity, p.p. 43-59, 1999.
[3] Jabbari, M.; Sohrabpour, S.; Eslami, M.R.; "Mechanical and Thermal Stresses in a Functionally Graded Hollow Cylinder Due to Radially Symmetric Loads", International Journal of Pressure Vessels and Piping, p.p. 493-497, 2002.
[4] 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", Journal of Applied Mechanics, p.p. 111-118, 2003.
[5] Awaji, H.; Sivakuman, R.; "Temperature and Stress Distributions in a Hollow Cylinder of Functionally Graded Material: The Case of Temperature-Dependent Material Properties", Journal of American Ceramic Society, p.p. 1059-1065, 2001.
[6] Liew, K.M.; Kitipornchai, S.; Zhang, X.Z.; Lim C.W.; "Analysis of the Thermal Stress Behavior of Functionally Graded Hollow Circular Cylinders",International Journal of Solids and Structures, p.p.2355-2380, 2003.
[7] Shakeri, M; Akhlaghi, M; Hoseini, S.M; "Vibration and radial wave propagation velocity in functionally graded thick hollow cylinder", Composite Structures,p.p. 174-181, 2006.
[8] Hoseini, S.M; Akhlaghi, M; Shakeri, M; "Dynamic response and radial wave propagation velocity in thick hollow cylinder made of functionally graded materials", Engineering Computations, p.p. 288-303,2007.
[9] Oral, A.; Anlas, G.; "Effects of radially varying moduli on stress distributionof nonhomogeneous anisotropic cylindrical bodies", International Journal of Solids and Structures, p.p. 5568–5588, 2005.
[10] Obata, Y.; Kanayama, K.; Ohji, T.; Noda, N.; "Two- Dimensional Unsteady Thermal Stresses in a Partially Heated Circular Cylinder Made of Functionally Graded Material", Proceeding of Thermal Stress, p.p. 13-17, 1999.
[11] Hoseini, S.M; Akhlaghi, M; Shakeri, M; "Transient heat conduction in functionally graded thick hollow cylinders by analytical method", Heat Mass Transfer, p.p. 669-675, 2007.
[12] Reddy, J.N,; Chin, C.D.; "Thermomechanical Analysis of Functionally Graded Cylinders and Plates", Journal of Thermal Stresses, p.p. 593–626,1998.
[13] حسینی، سید محمود؛ تحلیلهمزمانحرارتیمکانیکی پوستهاستوانهایجدارضخیمازجنسموادهدفمند )رسالهی دورهی دکتری(، شاکری، اخلاقی، دانشگاه . صنعتی امیرکبیر، تهران، 1386
[14] Obata, Y.; Noda, N.; "Steady Thermal Stresses in a Hollow Circular Cylinder and a Hollow Sphere of a Functionally Gradient Material", Journal of Thermal Stresses, p.p. 471-487, 1994.
[15] Ye, G.R.; Chen, W.Q.; Cai, J.B.; "A Uniformly Heated Functionally Graded Cylindrical Shell with Transverse Isotropy", Mechanics Research Communications, p.p. 535-542, 2001.
[16] Woo, J.; Meguid, S.A.; "Nonlinear Analysis of Functionally Graded Plates and Shallow Shells", International Journal of Solids and Structures, p.p. 7409-21, 2001.
[17] Ching, H.K.; Yen, S.C.; "Meshless Local Petrov-Galerkin Analysis for 2D Functionally Graded Elastic Solids Under Mechanical and Thermal Loads", Composites Part B, p.p. 223-240, 2005.