Elastic-Plastic Transition of Pressurized Functionally Graded Orthotropic Cylinder using Seth’s Transition Theory

Document Type: Research Paper


Department of Mathematics, Jaypee Institute of Information Technology, Noida, India


In this paper the radial deformation and the corresponding stresses in a functionally graded orthotropic hollow cylinder with the variation in thickness and density according to power law and rotating about its axis under pressure is investigated by using Seth's transition theory. The material of the cylinder is assumed to be non-homogeneous and orthotropic. This theory helps to achieve better agreement between experimental and theoretical results. Results has been mentioned analytically and numerically. From the analysis, it has been concluded that cylinder made up of orthotropic material whose thickness increases radially and density decreases radially is on the safer side of the design as circumferential stresses are high for cylinder made up of isotropic material as compared to orthotropic material. This paper is based on elastic-plastic behavior which plays important role in practical design of structures for safety factor.                       


[1] Bower A.F., 2009, Applied Mechanics of Solids, Taylor and Francis.
[2] Hearn E.J., 1997, Mechanics of Materials, Butterworth-Heinemann.
[3] Kim J.H., Paulino G.H., 2004, T-stress in orthotropic functionally graded materials: Lekhnitskii and Stroh formalisms, International Journal of Fracture 126: 345-384.
[4] Zenkour A.M., 2006, Rotating variable-thickness orthotropic cylinder containing a solid core of uniform-thickness, Archive Applied Mechanics 76: 89-102.
[5] Dag S., 2006, Thermal fracture analysis of orthotropic functionally graded materials using an equivalent domain integral approach, Engineering Fracture Mechanics 73: 2802-2828.
[6] Paschero M., Hyer M.W., 2009, Axial buckling of an orthotropic circular cylinder: Application to orthogrid conceptual, International Journal of Solids and Structures 46: 2151-2171.
[7] Wang H.M., 2010, Effect of material in-homogeneity on the rotating functionally of a graded orthotropic hollow cylinder, Journal of Mechanical Science and Technology 24(9): 1839-1844.
[8] Nie G.J., Batra R.C., 2010, Static deformations of functionally graded polar-orthotropic cylinders with elliptical inner and circular outer surfaces, Composites Science and Technology 70: 450-457.
[9] Sharma S., Yadav S., 2013, Thermo elastic-plastic analysis of rotating functionally graded stainless steel composite cylinder under internal and external pressure using finite difference method, Advances in Materials Science and Engineering 2013: 1-10.
[10] Gupta S.K., Bhardwaj P.C., 1986, Elastic plastic and creep transition in orthotropic rotating cylinder, Processing Indian National Science Academy 52(6): 1357-1369.
[11] Borah B.N., 2005, Thermo elastic plastic transition, Contemporary Mathematics 379: 93-111.
[12] Aggarwal A.K., Sharma R., Sharma S., 2013, Safety analysis using Lebesgue strain measure of thick-walled cylinder for functionally graded material under internal and external pressure, The Scientific World Journal 2013: 1-10.
[13] Sharma S., Sahai I., Kumar R. , 2014, Thermo elastic-plastic transition of transversely isotropic thick-walled circular cylinder under internal and external pressure, Multidiscipline Modeling in Materials and Structures 10: 211-227.
[14] Sharma S., Yadav S., Sharma R., 2017, Thermal creep analysis of functionally graded thick-walled cylinder subjected to torsion and internal and external pressure, Journal of Solid Mechanics 9(2): 302-318.