Computational procedure for determining the limiting values of the loading parameters of mechanical systems
DOI:
https://doi.org/10.7242/1999-6691/2011.4.4.45Keywords:
gradient system, potential function, separatrix, nonconvex potential, maximum loadsAbstract
A technique for calculating the limiting values of the loading parameters of mechanical systems with a finite number of elements is presented. The technique is based on the approximate method of constructing the separatrix of the potential functions of such systems. To illustrate the validity of the proposed approach, the problem of determining limiting loads applied to the rod system, which is used for triaxial stretching of an elementary cube made of nonlinear material, is solved.
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Vil’deman V.E., Sokolkin U.V., Taskinov A.A. Mehanika neuprugogo deformirovania i razrusenia kompozicionnyh materialov. - M.: Nauka, 1997. - 288 s.
Struzanov V.V., Mironov V.I. Deformacionnoe razuprocnenie materiala v elementah konstrukcij. - Ekaterinburg: UrO RAN, 1995. - 192 s.
Sedov L.I. Mehanika splosnoj sredy. T. 1. - M.: Nauka, 1970. - 492 s.
Struzanov V.V., Prosvirakov E.U., Burmaseva N.V. Ob odnom metode postroenia edinogo potenciala // Vycisl. meh. splos. sred. - 2009. - T. 2, No 2. - S. 96-107.
Gilmor R. Prikladnaa teoria katastrof: V 2-h kn. Kn. 1. - M.: Mir, 1984. - 350 s.
Horn R., Dzonson C. Matricnyj analiz.- M.: Mir, 1989. - 655 s.
Struzanov V.V. Ob ustojcivosti dvuhosnogo rastazenia kvadratnoj plastiny v odnoj gradientnoj mehaniceskoj sisteme // Trudy Instituta matematiki i mehaniki. - 2010. - T. 16, No 5. - S. 187-195.
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