Stability op circular cylindrical shells of variable thickness for a bending state of stress: PMM vol. 40, n≗ 2, 1976, pp. 376–383

Abstract

The stability problem of circular cylindrical shells of variable thickness under axial compression is examined, taking account of the bending stress of the initial pre-critical state. The initial bending equilibrium states of shells of variable thickness are described by nonlinear differential equations,and then a linearized system of stability differential equations with variable coefficients is obtained on the basis of [1, 2]. The variable coefficients reflect the influence of the initial bending state and the variability of the shell thickness. The nonlinear equations of the pre-critical state are solved by the small parameter method for an initial axisymmetric equilibrium mode. An iteration process to determine the critical forces is constructed by using the small parameter method on a linearized system of stability equations. The problem is solved in three approximations in the small parameters.