Static Analysis of Orthotropic Functionally Graded Material Cylinders with Finite Length by a Mesh-Free Method

Document Type : Persian


1 M.Sc. Graduated, Young Researchers Club, Khomeinishahr Branch, Islamic Azad University, Khomeinishahr, Iran

2 Assistant Professor, Mechanical Engineering Department, Razi University, Kermanshah, Iran

3 M.Sc. Graduated, Mechanical Engineering Department, Razi University, Kermanshah, Iran


In this paper static analysis of orthotropic functionally graded material (FGM) cylinders with finite length was carried out by a mesh-free method. MLS shape functions are used for approximation of displacement field in the weak form of equilibrium equation and essential boundary conditions are imposed by transformation method. In this simulation, an ax symmetric model is used. Mechanical properties of cylinders were assumed to be variable in the radial direction as a function of volume fraction. In this analysis, effects of the cylinder thickness and length, volume fraction exponent, type of materials layout and essential boundary conditions on displacement fields and stress distribution for orthotropic cylinders are investigated. The results of the proposed method for isotropic FGM cylinders were compared with corresponding results obtained from FEM and previous published works and a very good agreement are seen between them. Also by comparing the stress distributions of orthotropic FGM cylinders and corresponding results of homogeneous multilayered orthotropic cylinders were confirmed.


[1] Horgan C.O., Chan A.M., The pressurized hollow cylinder or disk problem for functionally graded isotropic linearly elastic materials, Journal of Elasticity, 55(1), 1999, pp. 43–59.
[2] Tutuncu N., Ozturk M., Exact solutions for stresses in functionally graded pressure vessels, Journal of Composite part B, 32(8), 2001, pp. 683-686.
[3] Jabbari M., Bahtui A., Eslami M.R., Axisymmetric mechanical and thermal stresses in thick long FGM cylinders, Journal of Thermal Stresses, 29(7), 2006, pp. 643–63.
[4] Tutuncu N., Stresses in thick-walled FGM cylinders with exponentially-varying properties, Engineering Structures, 29(9), 2007, pp. 2032-35.
[5] Li, X, Peng X., A Pressurized Functionally Graded Hollow Cylinder with Arbitrarily Varying Material Properties, Journal of Elasticity, 96, 2009, pp. 81-95.
[6] Tutuncu N., Temel B., A novel approach to stress analysis of pressurized FGM cylinders, disks and spheres, Composite Structures, 91(3), 2009, pp. 385-90.
[7] Nie G.J., Batra R.C., Static deformations of functionally graded polar-orthotropic cylinders with elliptical inner and circular outer surfaces, Composites Science and Technology, 70, 2010, pp. 450–457.
[8] Ye, J.Q., Sheng, H.Y., Free-edge effect in cross-ply laminated hollow cylinders subjected to axisymmetric transverse loads, International Journal of Mechanical Sciences, 45, 2003, pp. 1309–1326.
[9] Sobhani Aragh B., Yas, M. H., Static and free vibration analyses of continuously graded
fiber-reinforced cylindrical shells using generalized power-law distribution, Acta Mechanica, 215, 2010, pp. 155–173.
[10] Sladek J., Sladek, Zhang V., Stress analysis in anisotropic functionally graded materials by the MLPG method, Engineering Analysis with Boundary Elements, 29, 2005, pp. 597–609.
[11] Ching H.K. Yen, S.C. Meshless local Petrov-Galerkin analysis for 2d functionally graded elastic solids under mechanical and thermal loads, Journal  Composite part B, 36(3), 2005, pp. 223-40.
[12] Sladek J., Sladek V., Zhang Ch., Transient heat conduction analysis in functionally graded materials by the meshless local boundary integral equation method, Computational Materials Science, 28(3-4), 2003, pp. 494–504.
[13] Gilhooley D.F., Xiao, Batra J.R., McCarthy R.C., Two-dimensional stress analysis of functionally graded solids using the MLPG method with radial basis functions, Computational Materials Science, 41(4), 2008, pp. 467-81.
[14] Sladek V., Sladek J., Zhang Ch., Local integral equation formulation for axially symmetric problems involving elastic FGM, Engineering Analysis with Boundary Elements, 32(12), 2008, pp. 1012-24.
[15] Zhao X., Liew K.M., A mesh-free method for analysis of the thermal and mechanical buckling of functionally graded cylindrical shell panels, Computational Mechanics, 45, 2010, pp. 297–310.
[16] Foroutan M., Moradi-Dastjerdi R., Sotoodeh-Bahreini R., Static analysis of FGM cylinders by a mesh-free method, Steel and Composite Structures, 12, 2012, pp. 1-11.
[17] Mollarazi H.R., Foroutan M., Moradi-Dastjerdi R., Analysis of free vibration of functionally graded material (FGM) cylinders by a meshless method, Journal of Composite Materials, 46(5) 2011, pp. 507–515.
[18] مرادی دستجردی ر.، فروتن م.، پوراصغر ا.، تحلیل ارتعاشات آزاد و اجباری استوانه‌هایی ازجنس مواد هدفمند به روش بدون المان، فصلنامه علمی پژوهشی مهندسی مکانیک جامدات، شماره 5، 1388، صص 77-69.