DEFINING RELATION OF NONLINEARLY ELASTIC-VISCOPLASTIC MATERIAL WITH REFERENCE TO METALS AND ALLOYS

Shwed O.L., United Institute of Informatics Problems of NAS of Belarus; Minsk, the Republic of Belarus

Overall principles of build-up of the physical equations are offered. Essential modeling hypotheses are made. The statement of a defining relation for considered model of a material is given. The example of a numerical modeling of process of simple shearing strain is resulted.

Elastic-viscoplastic material, defining relation

• Shwed O.L., Abramov A.A. Matematicheskoe modelirovanie processa prjamogo vydavlivanija svinca [Mathematical modeling of direct extrusion of lead]. Informatika [Computer science], 2007, no. 4(16), pp. 133-136.
• Levitas V.I. Bolshie uprugoplasticheskie deformacii materialov pri vysokom davlenii [The large elastic-plastic deformation of materials under high pressure]. Kiev, Nauk. dumka Publ., 1987. 232 p.
• Naghdi P.M. A critical review of the state of finite plasticity. ZAMP, 1990, vol. 41, no. 3, pp. 315-394.
• Murnagan F.D., Dover N.Y. Finite deformation of an elastic solid. 1967. 140 p.
• Lure A.I. Nelinejnaja teorija uprugosti [Nonlinear Theory of Elasticity]. Moscow, Nauka Publ., 1980. 512 p.
• Bell Dzh.F. Jeksperimentalnye osnovy mehaniki deformiruemyh tverdyh tel. Ch. II: Konechnye deformacii [Experimental foundations of the mechanics of deformable solids. Part II: Finite strain]. Moscow, 1984. 432 p.
• Shwed O.L. K teorii uprugoplastichnosti pri konechnyh uprugih deformacijah i povorotah [On the theory of elastic-plastic at the end of the elastic deformation and bends]. Dokl. NAN Belarusi [Reports of NASB], 2005, vol. 49, no. 3, pp. 45-48.
• Zhilin P.A. Matematicheskaja teorija neuprugih sred [The mathematical theory of elastic media]. Uspehi mehaniki [Mechanics advances], 2003, no. 4, pp. 3-36.
• Pezhina P. Osnovnye voprosy vjazkoplastichnosti [Key questions of viscoplastic]. Moscow, Mir Publ., 1968. 176 p.
• Pozdeev A.A., Trusov P.V., Hyashin Yu.I. Bolshie uprugoplasticheskie deformacii: teorija, algoritmy, prilozhenija [The large elastic-plastic deformation theory, algorithms, applications]. Moscow, Nauka Publ., 1986. 232 p.
• Shwed O.L. Dvojstvennoe opisanie uprugoplasticheskogo processa [The dual description of elastic-plastic process]. Vestn. BGU [BSU herald], 2007, vol. 1, no. 2, pp. 88-93.
• Shwed O.L. Ob uchete jeffekta Baushingera v modeli uprugoplasticheskoj sredy [On account Baushinger effect in elastic-plastic medium model]. Informatika [Computer science], 2006, no. 3(11), pp. 24-27.
• Shwed O.L., Opredelenie poverhnosti tekuchesti s uchetom vlijanija vjazkosti[Determination of the yield surface, taking into account the effect of viscosity]. Dokl. NAN Belarusi [Reports of NASB], 2007, vol. 51, no. 6, pp. 35-39.
• Shwed O.L. Ob obektivnosti uravnenij v nelinejnyh teorijah deformiruemogo tverdogo tela [On the objectivity of equations in nonlinear theories of deformable solids]. ]. Vestn. BNTU [BSTU herald], 2008, no. 1, pp. 57-60.
• Shwed O.L., Makhnach V.I. Chislennoe modelirovanie bol'shih deformacij i povorotov uprugoplasticheskoj sredy [Numerical simulation of large deformation and rotation elastic-plastic medium]. Informatika [Computer science], 2005, no. 1(5), pp. 24-27.

ON THE INFLUENCE OF MODULUS OF SUBGRADE REACTION AND THE WAVELENGTH OF CORRUGATION ON BIFURCATION OF THIN CORRUGATED SHELL LYING ON ELASTIC FOUNDATION UNDER ACTION OF HYDROSTATIC PRESSURE

Kuntsevich S.P., Candidate of Physical and Mathematical Sciences; Vitebsk State University named after P.M. Masherov; Vitebsk, the Republic of Belarus

Nikonova T.V., Vitebsk State Technological University; Vitebsk, the Republic of Belarus

Mikhasev G.I., Doctor of Physical and Mathematical Sciences; Belarusian State University, Minsk, the Republic of Belarus, E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.">This email address is being protected from spambots. You need JavaScript enabled to view it.

The problem of buckling of a thin corrugated shell lying on elastic foundation under action of the non-uniform hydrostatic pressure is considered. The influence of the elastic foundation is taken into account as the additional pressure within the framework of Winkler`s model. The semi-moment equations of the thin elastic shell theory are assumed as the governing ones. The rigid clamped conditions are considered at the edges of the shell. Assuming that the hydrostatic pressure depends upon the circumferential co-ordinate, solutions of the governing equations are constructed in the form of functions decaying far from some generator on the shell surface. Using the complex WKB-method, the boundary-value problem is reduced to the sequence of the one-dimensional boundary-value problems. Its numeric solution has been obtained. The influence of parameters of corrugation of the shell and modulus of subgrade reaction on the critical pressure has been analyzed.

Corrugated shell lying, hydrostatic pressure, WKB-method, elastic foundation

• Volmir A.S. Ustojchivost deformiruemyh system [The stability of deformable systems]. Moscow, Nauka Publ., 1967. 984 p.
• Grigolyuk E.I., Kabanov V.V. Ustojchivost obolochek [Shells resistance]. Moscow, Nauka Publ., 1978. 360 p.
• Tvostik P.E. Ustojchivost tonkih obolochek [Thin Shells resistance]. Moscow, Nauka Publ., 1995. 320 p.
• Ilgamov M.A., Ivanov V.A., Gulin B.V. Prochnost, ustojchivost i dinamika obolochek s uprugim zapolnitelem [The strength, stability and dynamics of shells with elastic filler]. Moscow, Nauka Publ., 1977. 332 p.
• Tvostik P.E. Lokalnaja ustojchivost plastin i pologih obolochek na uprugom osnovanii [Local stability of plates and shallow shells on elastic foundation]. Izv. RAN. Mehanika tverdogo tela [Herald of Russian Academy of Sciences. mechanics of rigid body], 2005, no. 1, pp. 147-160.
• Mikhasev G.I., Nikonova T.V. Ustojchivost tonkih gofrirovannyh cilindricheskih obolochek, lezhashhih na uprugom osnovanii pod dejstviem odnorodnogo gidrostaticheskogo davlenija [Stability of thin corrugated cylindrical shells lying on an elastic foundation under the action of a uniform hydrostatic pressure]. Vestn. Viteb. gos. un-ta [Herald of Vitebsk State University], 2007, no. 3, pp. 112-117.
• Nikonova T.V., Kuntsevich S.P., Mikhasev G.I. O bifurkacii tonkoj gofrirovannoj obolochki s uprugim zapolnitelem pod dejstviem neodnorodnogo gidrostaticheskogo davlenija [The bifurcation of thin corrugated shell with elastic filler under the action of hydrostatic pressure inhomogeneous]. Mehanika mashin, mehanizmov i materialov [Mechanics of machines, mechanisms and materials], 2008, no. 3, pp. 48-51.
• Korbut B.A., Nagorny Yu.N. Ob odnoj modeli zapolnitelja v zadachah ustojchivosti cilindricheskih obolochek [On a model of aggregate in problems of stability of cylindrical shells]. Izv. vuzov. Mashinostroenie [Math. Engineering colleges], 1971, no. 6, pp. 16-21.
• Korenev B.G. Voprosy rascheta balok i plit na uprugom osnovanii [Questions about calculation of beams and plates on elastic foundation]. Moscow, Gosstroyizdat Publ., 1954. 232 p.
• Mikhasev G.I., Nikonova T.V. Ocenka usilij v tonkostennoj gofrirovannoj trube s uprugim zapolnitelem pod dejstviem peremennogo davlenija [Evaluation efforts in thin-walled corrugated pipe with elastic filler under the influence of alternating pressure]. Ves. Nac. akad. navuk Belarusi. Ser. fiz.-tjehn [Herald of NAS of Belarus. Phys-tech. series], 2005, no. 4, pp. 55-60.
• Frese M.V. Vzaimodejstvie metallicheskih gofrirovannyh konstrukcij s gruntovoj sredoj. Diss. kand. tekh. nauk [Interaction of corrugated metal structures with soil environment. Cand. techn. sci. diss.]. St. Petersburg, 2006. 162 p.

DISRUPTION OF CORRODED ROD WITH PIECEWISE CONSTANT THICKNESS UNDER DYNAMIC LONGITUDINAL LOADING

Akhoundova I.A., Azerbaijan Technical University; Baku, Azerbaijan

The present paper considers longitudinal oscillations of corroded rod with piecewise constant thickness taking initial stress into account. The value of proper frequency is defined. In addition, the value of the frequency when the rod breaks in the place of connection of rod elements is defined.

Longitudinal oscillations, corroded rod, proper frequency

• Vasidzu K. Variacionnye metody v teorii uprugosti i plastichnosti [Variational methods in the theory of elasticity and plasticity]. Moscow, Mir Publ., 1987. 542 p.
• Ovchinnikov I.G., Petrov V.V. Matematicheskoe modelirovanie processa vzaimodejstvija jelementov konstrukcii s agressivnymi sredami [Mathematical modeling of the interaction of structural elements with aggressive media]. Mezhvuz. nauch. sb.“Deformirovanie materialov i jelementov konstrukcij v agressivnyh sredah“ [International scientific collection: The deformation of materials and structures in aggressive environments]. Saratov, SPI Publ., 1983/ pp. 3-11.

CALCULATION OF PARAMETRIC VIBRATIONS OF HOMOGENEOUS IN THICKNESS VISCO-ELASTIC BAR IN VISCO-ELASTIC SOIL

Pirmamedov I.T., Candidate of Physical and Mathematical Sciences; Institute of Mathematics and Mechanics of National Academy of Sciences of Azerbaijan, Baku, Azerbaijan

In the present paper we consider parametric vibrations of rectilinear inhomogeneous in thickness bar allovering for physical and geometrical non-linearity, buried under visco-elastic soil. The problem is solved by variational method typical curves for dependence of applied force on frequency are constructed.

Parametric vibration, thickness visco-elastic bar, visco-elastic soil

• Pasternak P.L. Osnovy novogo metoda rascheta fundamentov na uprugom osnovanii pri pomoshhi dvuh kojefficientov posteli [Fundamentals of the new method of calculation of foundations on an elastic foundation with two bed coefficients].Moscow, Gosstroyizdat Publ., 1954. 56 p.
• Alizade A.N., Amenzade R.Yu. Variacionnyj princip nelinejno-vjazko-uprugosti s uchetom geometricheskoj nelinejnosti [The variational principle of nonlinear viscoelastic considering geometric nonlinearity]. DAN SSSR [DAN USSR], 1976, vol. 230, no. 6, pp. 1303-1305.
• Yusifov M.O. K raschetu pokrytija truboprovodov pri pul'sirujushhem davlenii [On the calculation pipe coating with a pulsating pressure]. Neft I gas [Oil and gas], 1985, no. 10, pp. 61-64.
• Volmir A.S. Ustojchivost deformiruemyh system [The stability of deformable systems]. Moscow, Nauka Publ., 1967. 984 p.
• Volmir A.S. Nelinejnaja dinamika plastinok i obolochek [Nonlinear dynamics of plates and shells]. Moscow, Nauka Publ., 1972. 432 p.