Analytical and Finite Element Stress Analysis of Pressure Vessels under Constant and Cyclic Loading

Abstract

Pressure vessels are wildly used in many fields, such as chemical, petroleu m, military industries as well as in nuclear power plants. Pressure vessels should be designed with great care because rupture of pressure vessel may cause catastrophic accident. The common problem to the pressure vessel's designer is the accurate evaluation of stresses due to the applied mechanical and /or thermal loads. The finite element method FEM is one of the nu merical stress analysis for many subjects. In this paper a complete stress analysis through the wall of pressure vessel under the effect of constant and cyclic loading is presented. Hoop, radial, axial and effective stresses for cylindrical pressure vessels have been evaluated analytically as well as using the program package ANSYS as a nu merica l fin ite element method. A comparison between the analytical and numerical solution is presented, and it is found a good agreement between them. NOTATION E … …. Young's modulus of material Mpa í µí±“ …. Frequency of pressure oscillation s −1 H = E α ∆T 1 − ѵ …. Thermal load Mpa K = r o r i … … Diamter ratio K i = r c r i … Diameter ratio for inner cylinder K o = r o r c … Diameter ratio for outer cylinder P a = P i max − P i min 2. . Pressure amplitude Mpa P c … … Contact pressure Mpa P i …. . Applied internal pressure Mpa P m = P i max + P i min 2 … Mean pressure Mpa P o … External pressure Mpa P r i ,t. Pressure at inner surface r i and after time t Mpa í µí±Ÿ … … Desired radius mm r c …. Contact radius of the cylinder mm r i …. . Inner radius of the cylinder mm r o …. Outer radius of the cylinder mm R = r r i … Normalized radius t … …. . Time s T …. Temperature at any radius of the cylinder ℃ _____________________________________________ T i …. Temperature at inner surface of the cylinder ℃ T o … Temperature at outer surface of the cylinder ℃ ∆T = T i − T o …. . Temperature difference ℃ α … … Coefficient of linear thermal expansion mm −1 ℃ −1 σ …. Stress Mpa í µí¼Ž í µí±Ž …. Stress amplitude Mpa σ h …. Hoop stress Mpa σ m …. Mean stress Mpa σ r …. Radial stress Mpa σ v …. Equivalent stress Mpa σ z …. Axial stress Mpa ѵ … … Poisson's ratio t = í µí±“t …. …...Normalized time σ = σ P … …. . Normalized stress σ h = σ h P …. . Normalized hoop stress σ r = σ r P … … Normalized radial stress σ v = σ v P …. . Normalized equivalent stress σ z = σ z P … … Normalized axial stress