Planar problem of stability loss under stretching

Zbigniew Wesołowski

Aplikace matematiky (1965)

  • Volume: 10, Issue: 1, page 1-14
  • ISSN: 0862-7940


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.

How to cite


Wesołowski, Zbigniew. "Rovinný problém ztráty stability v tahu." Aplikace matematiky 10.1 (1965): 1-14. <>.

author = {Wesołowski, Zbigniew},
journal = {Aplikace matematiky},
keywords = {mechanics of solids},
language = {cze},
number = {1},
pages = {1-14},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Rovinný problém ztráty stability v tahu},
url = {},
volume = {10},
year = {1965},

AU - Wesołowski, Zbigniew
TI - Rovinný problém ztráty stability v tahu
JO - Aplikace matematiky
PY - 1965
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 10
IS - 1
SP - 1
EP - 14
LA - cze
KW - mechanics of solids
UR -
ER -


  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). (1952) Zbl0046.41208MR0047486
  2. W. Urbanowski, Small deformations superposed on finite deformation of a curvilinearly orthotropic body;, Arch. Mech. Stos., 2, 11 (1959). (1959) Zbl0088.16405MR0105870
  3. A. E. Green W. Zerna, Theoretical Elasticity;, Oxford 1954. (1954) Zbl0056.18205MR0064598
  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). (1963) Zbl0119.40002MR0157537
  5. Z. Wesolowski, Some problems of stability in tension in the light of the theory of finite strain;, Arch. Mech. Stos., 6, 14 (1962). (1962) Zbl0109.17105MR0149744

NotesEmbed ?


You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.


Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.