CALCULATION OF CRITICAL AXIAL RELATED EFFORTS OF ISOTROPIC CYLINDRICAL SHELLS

Abstract

The theory of stability of a circular cylindrical shell of a certain length and radius is studied, taking into account the thickness of the cylinder walls. In the study of the cylinder is loaded at the edges evenly distributed compressive forces. A design scheme was constructed and a method for calculating the critical axial compressive forces was proposed. The basic data are: the shell is geometrically perfect, the shell material is ideally elastic, the pre-critical state of the shell is membrane less, the edges of the shell are freely supported. The method of solving the problem is proposed – energetic using relations of the linear theory of shells.

Minimizing the proposed ratios by integer parameters allows finding the values of critical loads in absolute and relative values for thin-walled cylindrical shells of any geometrical dimensions.

An approach is presented in which it is assumed that the loss of stability of the shell occurs due to the internal energy accumulated in the subcritical state, and the work of external loads at the moment of loss of stability is zero. The considered approach is absolutely different from the known ones, where it was assumed that the change in the potential energy of axial tension-compression is equal to the work of external axial forces on displacements obtained by stretching-compression of the middle surface of the shell at the moment of loss of stability. Both approaches suggest that the critical load changes at the moment of loss of resilience.

The peculiarity of the proposed approach is to take into account changes in the external load with loss of stability of the shell and the assumption that the change in the potential energy of axial tension – compression is equal to the additional work of external axial forces on axial displacements obtained by tension – compression of the middle surface of the shell.

The proposed approach leads to results that qualitatively and quantitatively describe the phenomena observed in experiments.

An analytical dependence of the critical forces on the geometry of the shell and the parameters of wave formation is obtained.

It is shown that the relative values of axial critical loads significantly depend on the change in the ratio of the radius of the shell to its thickness and length to radius.