On the stability of elastic compressible bodies under all-around compression: PMM vol. 42, no. 5, 1978, pp. 936–945

Abstract

The stability of simply -connected isotropic compressible elastic bodies with an arbitrary form of the elastic potential subjected to uniform all-around compression is investigated. The three-dimensional linearized theory of elastic stability for finite and small precritical deformations is involved. The case is considered when the body surface consists of two parts, one of which is rigidly clamped or hinged. It is proved that the equilibrium state will be stable if the pressure is applied in the form of a “follower” load on the second part of the surface, and is unstable if the pressure is applied in the form of a “dead” load on this part of the surface. In the latter case, the critical load for thinwalled bodies is approximately half the Euler force. Examples are considered for rectangular and circular plates, as well as for a circular rod in the case of materials with different forms of the elastic potential. After the paper [1] had been published, the question of the stability of isotropic compressible simply-connected bodies under all-around compression was considered in numerous papers from different aspects of the three-dimensional theory of stability under small and finite precritical deformations. The disagreement between the results from these theories was explained by the inaccuracies of the theory of small precritical deformations. Results have been obtained in [2,3] in general form for the theory of finite and small precritical deformation, and a survey of investigations on the problem considered is presented in [2].