Stateczność pełnego sprężystego walca przy dużych odkształceniach
Stability of a fully-elastic cylinder at large deformations
The paper considers the stability of a full circular cylinder subjected to a finite stretching or compressing. It is assumed that the cylinder material is elastic and compressible with a completely arbitrary physical characteristic. The method of small deformations superposed on the initial finite deformations is used. After the linearization of the relationships for a small additional deformation a set or partial differential equations was obtained, which upon the decomposition of the functions sought for into a Fourier series became reduced to a set of ordinary differential equations. The general solution of this set of equations has been found. The boundary conditions were constructed for a load vertical to the front surfaces, and the lateral surfaces are not under load.
The conditions of loss of stability are given corresponding to the above mentioned manner or loading.
References
A.E. Green, R.S. Rivlin, R.T. Shield, General theory of small elastic deformnations superposed on finite elastie deformation, Proc. Roy. Soc., A211 (1952).
A.E. Green, W. Zerna, Theoretical Elasticity, Oxford 1954.
Z. Wesołowski, The symmetric problem of stability loss of an elastic bar subject to tension, Arch. Mech. Stos., 3, 15 (1963).
G. Zhong-Heng, W. Urbanowsk1, Stability of non-conservative systems in the theory of elasticity of finite deformations, Arch. Mech. Stos., 2, 15 (1963).