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Limit Dependences in Stability Calculations With Account for Physical Nonlinearity

Published online by Cambridge University Press:  13 September 2016

J. Rutman  and
V. Ulitin
J. Rutman*
Affiliation:
Saint Petersburg State University of Architecture and Civil EngineeringSt. Petersburg, Russia
V. Ulitin
Affiliation:
Saint Petersburg National Research University of Information Technologies, Mechanics and OpticsSt. Petersburg, Russia
*
*Corresponding author ([email protected])
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Abstract

Stability of bars, plates, shells, and other thin-walled structures in conditions of small physical nonlinearity is considered, when stresses exceed the proportionality limit, the amount of deformations being limited. Shanley's concept is used. The critical state is determined by means of some limit dependences. In a large number of cases, when creating efficient highly-stressed constructions, limited plastic deformations are allowed in them. When analysing stability in the critical state, the calculated stresses turn out to exceed the proportionality limit and the Young's modulus of elasticity turns out to be greater than the tangent modulus corresponding to the calculated stress on the diagram “deformation-stress”. The objective of this work is to show that stability calculation beyond the proportionality limit is reduced to the analysis of some limit dependences as well as to develop a general solution algorithm for similar problems.

Keywords

Physical nonlinearityCritical stateLimit dependence
Type
Research Article
Information
Journal of Mechanics , Volume 33 , Issue 2 , April 2017 , pp. 157 - 160
Copyright
Copyright © The Society of Theoretical and Applied Mechanics 2017 

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References

1. Karpov, V. and Maslennikov, A., “Methods for Solving Non-Linear Tasks for Calculating Construction Structures”, World Applied Sciences Journal, 23 (Problems of Architecture and Construction), pp. 178–183 (2013).Google Scholar
2. Rutman, Y. and Kondratieva, L., “Calculation of Parameters of Buildings n Seismic Insulation System with Non-Linear Characteristics”, World Applied Sciences Journal, 23 (Problems of Architecture and Construction), pp. 127–132 (2013).Google Scholar
3. Ulitin, V.V., Fizicheski nelineynyy analiz ustoychivosti konstruktsiy [Physically nonlinear analysis of structural stability], Publishing House GIORD, Saint Petersburg, p. 96 (2007).Google Scholar
4. Gastev, V.A., Kratkiy kurs soprotivleniya materialov [Short course of resistance of materials.], 2nd Edition, Publishing House Nauka, Moscow, p. 456 (1977).Google Scholar
5. Papkovich, P.F., Teoriya uprugosti [Elasticity theory], Publishing House Oborongiz, Leningrad, p. 640 (1939).Google Scholar