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Keywords:
mechanics of solids
mechanics of solids
Summary:
The stability of a parallelepiped subjected to finite stretching is investigated. The materials is assumed to be elastic an orthotropic, with arbitrary non-linear physical properties.
The deformation is divided into two parts: a finite initial deformation and a small additional deformation. All the relations which correspod to the additional deformation are linearized. After expanding the additional displacements into series, an ordinary differential equation with corresponding boundary conditions is obtained. Eigenvalues of this boundary problem are the sought-for critical elongations.
It is proved that in the case, when the length of the parallelepiped tends to infinity, loss of stability occurs when the stretching force attains its maximum.
References:
[1] A. E. Green R. S. Rivlin R. T. Shield: General theory of small elastic deformations superposed on finite elastic deformations. Proc. Roy. Soc. A 211 (1952). MR 0047486
[2] W. Urbanowski: Small deformations superposed on finite deformation of a curvilinearly orthotropic body. Arch. Mech. Stos., 2, 11 (1959). MR 0105870
[3] A. E. Green W. Zerna: Theoretical Elasticity. Oxford 1954. MR 0064598
[4] Guo Zhong-heng W. Urbanowski: Stability of non-conservative systems in the theory of elasticity of finite deformations. Arch. Mech. Stos., 2, 15, (1963). MR 0157537
[5] Z. Wesolowski: Some problems of stability in tension in the light of the theory of finite strain. Arch. Mech. Stos., 6, 14 (1962). MR 0149744
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