A numerical method for the CREEP analysis of thin cylindrical shells

Abstract

The objective of this thesis is to present the governing equations for the creep analysis of thin cylindrical shells. A numerical model for steady-state creep conditions is presented using von Mises' criterion and the power law of creep. The proposed numerical procedure is based on Chaplygin's extension of Newton's method coupled with a finite difference approach. Expressions for stresses, membrane forces and bending moments in terms of displacements are linearized by expanding them in the vicinity of certain approximate values of displacement. Substitution of these expressions into the equations of equilibrium then reduces the problem into a set of simultaneous linear differential equations with respect to the small corrections of displacement. The solution of this set leads to improved approximate values. When these approximate values converge to certain values with sufficient accuracy by iteration, an accurate solution for displacements is thus obtained. On the basis of the proposed method, original numerical results are reported for circular cylindrical shells which are square-in-plan, fixed at ail edges and subjected to normal internal pressure. The proposed method is shown, using the present generation of digital computers, to be a powerful means for the creep analysis of such types of structures.