Collapse Pressure Analysis of Transversely Isotropic Thick-Walled Cylinder Using Lebesgue Strain Measure and Transition Theory

Abstract

The objective of this paper is to provide guidance for the design of the thick-walled cylinder made up of transversely isotropic material so that collapse of cylinder due to influence of internal and external pressure can be avoided. The concept of transition theory based on Lebesgue strain measure has been used to simplify the constitutive equations. Results have been analyzed theoretically and discussed numerically. From this analysis, it has been concluded that, under the influence of internal and external pressure, circular cylinder made up of transversely isotropic material (beryl) is on the safer side of the design as compared to the cylinders made up of isotropic material (steel). This is because of the reason that percentage increase in effective pressure required for initial yielding to become fully plastic is high for beryl as compared to steel which leads to the idea of “stress saving” that reduces the possibility of collapse of thick-walled cylinder due to internal and external pressure.

Secondary Creep Analysis of FG Rotating Cylinder with Exponential, Linear and Quadratic Volume Reinforcement

“…Pressurized water reactors use circular cylinders with both, internal and external pressure and having isotropic material properties. In a steam generator tube, an external pressure can be used to assist the flow of primary coolant outside the cylindrical tube whereas internal pressure can assist the secondary water flow inside the cylindrical tube [ 25 ]. In such working conditions, material strength or safety factor, under pressure loads together with other surface and body forces, is to be critically analyzed to avoid the bursting or rupture of the pressurized cylindrical body [ 27 ].…”

“…From Equations ( 14) and ( 17) axial stress σ z and tangential stress σ θ , respectively, in a rotating cylinder with linear volume reinforcement can be obtained. The radial and tangential strain rates in a rotating cylinder under linear volume reinforcement can be obtained from Equations ( 13) and (25).…”

“…For rotating cylinder with quadratic volume reinforcement, the expression for axial stress σ z and tangential stress σ θ can be obtained using Equations ( 14) and (17), respectively. Further, radial and tangential strain rates can be obtained from Equations ( 13) and (25).…”

“…Rearchers have used various mathematical methods such as Runge Kutta 4th order, finite difference method (FDM), shooting method, complementary function method (CFM), homotopy analysis method for obtaining the solution of steady state creep in disks and cylinders made up of functionally graded materials. Creep models based on iterative technique, finite element method (FEM) and Seth’s transition theory for obtaining stress distribution in functionally graded rotating disks and cylinders can be also found in the literature [ 23 , 24 , 25 ]. Nie and Batra [ 26 ] studied the problem of material tailoring to obtain desired stress field in hollow cylinder made up of functionally graded in-compressible material with radially varying shear modulus.…”