### ENERGY METHOD OF ANALYSIS OF STABILITY OF COMPRESSED RODS WITH REGARD FOR CREEPING

Pages 101-108

The problem of stability of polymer rods with account for creeping was resolved using the energy method customized by Tymoshenko and Ritz. Possible patterns of displacements were provided in the form of trigonometric series with undetermined coefficients. The principle of the minimal total potential energy of the system was taken as the basis. According to this principle, the form in which the potential energy has a minimum value is implemented in all possible patterns of deformation occurring due to the loss of stability. The energy method makes it possible to replace the solution of complex differential equations by the solution of simple linear algebraic equations. The result was obtained numerically using MatLab software applicable to different equations describing deformations and stresses caused by the exposure to creeping. The problem was solved for low and high density polyethylene. The equation of Maxwell and Thompson was

DOI: 10.22227/1997-0935.2013.1.101-108

- Aleksandrov A.V. Soprotivlenie materialov. Osnovy teorii uprugosti i plastichnosti [Strength of Materials. Fundamentals of the Theory of Elasticity and Plasticity]. Moscow, Vyssh. shk. publ., 2002, 400 p.
- Klimenko E.S., Amineva E.H., Litvinov S.V., Yazyev S.B., Kulinich I.I. Ustoychivost’ szhatykh neodnorodnykh sterzhney s uchetom fi zicheskoy nelineynosti materiala [Stability of Compressed Heterogeneous Rods with Account for the Physical Nonlinearity of the Material]. Rostov-on-Don, Rostov State University of Civil Engineering Publ., 2012, 77 p.
- Alfutov N.A. Osnovy rascheta na ustoychivost’ uprugikh system [Fundamentals of Stability Analysis of Elastic Systems]. Moscow, Mashinostroenie Publ., 1991, 336 p.
- Vol’mir A.S. Ustoychivost’ deformiruemykh system [Stability of Deformable Systems]. Moscow, Nauka Publ., 1975, 984 p.
- Timoshenko S.P. Ustoychivost’ uprugikh system [Stability of Elastic Systems]. Moscow, Gostekhizdat Publ., 1946.
- Andreev V.I. Nekotorye zadachi i metody mekhaniki neodnorodnykh tel [Some Problems and Methods of Mechanics of Heterogeneous Bodies]. Moscow, ASV Pub., 2002, 288 p.
- Turusov R.A. Temperaturnye napryazheniya i relaksatsionnye yavleniya v osesimmetrichnykh zadachakh mekhaniki zhestkikh polimerov [Thermal Stresses and Relaxation Phenomena in Axisymmetric Problems of Mechanics of Rigid Polymers]. Moscow, 1970, 104 p.
- Belous P.A. Ustoychivost’ polimernogo sterzhnya pri polzuchesti s uchetom nachal’noy krivizny [Stability of a Polymer Rod Exposed to Creeping with Regard for Its Initial Curvature]. Trudy Odesskogo politekhnicheskogo instituta [Works of Odessa Polytechnic Institute]. 2001, no. 2, pp. 43—46.
- Gurevich G.I. Deformiruemost’ sred i rasprostranenie seysmicheskikh voln [Deformability of Media and Propagation of Seismic Waves]. Moscow, Nauka Publ., 1974, 482 p.
- Gol’dman A.Ya. Prochnost’ konstruktsionnykh plastmass [Structural Plastic Strength]. Leningrad, Mashinostroenie Publ., 1979, 320 p.