| Abstract: | Conclusion In 8, 9] and in the present paper we analyzed the possibilities of using the approximate approach 15, 18] in the three-dimensional stability theory of deformable bodies as applied to effects of internal and surface instability and to stability of thinwalled structural elements. The analysis mentioned has been performed by comparing for standard problems the results obtained by the approximate approach 15, 18] with the results for the similar problems, obtained within the three-dimensional linearized stability theory of deformable bodies (for example 2–5, 7, 10, 19]), constructed with the accuracy usually adopted in mechanics. The following conclusions are drawn as a result of the analysis.Applied to effects of internal and surface instability, the approximate approach leads to result in disagreement with the corresponding results of the three-dimensional linearized stability theory of deformable bodies.As applied to the study of stability of thin-walled structural elements, the use of the approximate approach is justified if we restrict ourselves to a calculational accuracy of critical loads corresponding to that of the Kirchhoff-Love hypothesis.In connection with the discussion above, numerous publications carried out on the basis of the approximate approach require further study to clarify the validity limits of the results obtained.Institute of Mechanics, Academy of Sciences of the Ukrainian SSR, Kiev. Translated from Prikladnaya Mekhanika, Vol. 22, No. 2, pp. 3–17, February, 1986. |
