An approximate algorithm for solving the problems of linear viscoelasticity
DOI:
https://doi.org/10.7242/1999-6691/2012.5.3.34Keywords:
effective modulus, constitutive equations, linear viscoelasticity, stress and strain tensors, creep and relaxation operators, relative error, mass fraction, variational problems, boundary-value problemsAbstract
This study is devoted to the development of approximate methods for solving the problems of linear elasticity theory. Based on the timeeffective moduli of Lagrangian and Castilian types obtained in early works, two pairs of unique effective characteristics of isotropic bodies are determined. In accordance with the known approach of mechanics of composite materials, the viscoelastic body is assumed to be a twocomponent composite, one component of which has the properties defined by the pair of effective moduli of Lagrangian type, and the characteristics of the second component are set by the pair of Castilian-type moduli. By averaging these characteristics according to Voigt Reyscu, expressions are written for two-component effective moduli. The mass fraction of one of the components is given as a function of time. A comparison of the approximate solutions obtained using the proposed effective moduli with the analytical solutions demonstrates their coincidence within 5% for two problems.
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References
Dej U.A. Termodinamika prostyh sred s pamat’u. - M.: Mir, 1974. - 190 s.
Kravcuk A.S., Majboroda V.P., Urzumcev U.S. Mehanika polimernyh i kompozicionnyh materialov. - M.: Nauka, 1985. - 304 s.
Trusdell K. Pervonacal’nyj kurs racional’noj mehaniki splosnyh sred - M.: Mir, 1975. - 592 s.
Il’usin A.A., Pobedra B.E. Osnovy matematiceskoj teorii termovazkouprugosti. - M.: Nauka, 1970. - 280 s.
Blend D.R. Teoria linejnoj vazkouprugosti. - M.: Mir, 1965. - 199 s.
Il’usin A.A. Metod approksimacij dla rasceta konstrukcij po linejnoj teorii termovazkouprugosti // Mehanika polimerov. - 1968. - No 2. - S. 210-221.
Adamov A.A., Matveenko V.P., Trufanov N.A., Sardakov I.N. Metody prikladnoj vazkouprugosti. - Ekaterinburg: UrO RAN, 2003. - 411 s.
Hutoranskij N.M. Metod granicno-vremennyh integral’nyh uravnenij v nestacionarnyh dinamiceskih zadacah vazkouprugosti // Prikladnye problemy procnosti i plasticnosti. Vsesouz. mezvuz. sb. / Gor’k. un-t, 1979. - No 12. - S. 11-17.
Pestrenin V.M., Pestrenina I.V., Kostromina P.P. Vlianie razgruzocnyh selej na naprazennoe sostoanie i polzucest’ porodnogo massiva v okrestnosti vyrabotki // Vycisl. meh. splos. sred. - 2011. - T. 4, No 2. - S. 110- 118. DOI
Pavlov S.M., Svetaskov A.A. Iteracionnyj metod resenia zadac linejnoj vazkouprugosti // Izvestia VUZov. Fizika. - 1993. - T. 36, No 4. - S. 129-137.
Kulikov R.G., Trufanov N.A. Iteracionnyj metod resenia kvazistaticeskih nelinejnyh zadac vazkouprugosti // Vycisl. meh. splos. sred. - 2009. - T. 2, No 3. - S. 44-56. DOI
Kovalenko A.D., Kil’cinskij A.A. O metode peremennyh modulej v zadacah linejnoj nasledstvennoj uprugosti // Prikladnaa mehanika. - 1970. - T. 6, No 12. - S. 27-34.
Malyj V.I., Trufanov N.A. Metod kvazikonstantnyh operatorov v teorii vazkouprugosti anizotropnyh nestareusih materialov // Izv. AN SSSR. MTT. - 1987. - No 6. - S. 148-154.
Mal’cev L.E., Krenkin V.I. Metod neposredstvennogo resenia zadac vazkouprugosti // Mehanika polimerov. - 1977. - No 4. - S. 606-613.
Svetaskov A.A. Opredelenie effektivnyh harakteristik neodnorodnyh vazkouprugih tel // ZVT. - 2001. - T. 6, No 1. - S. 52-64.
Svetaskov A.A. Effektivnye po vremeni moduli linejnoj vazkouprugosti // Mehanika kompozitnyh materialov. - 2000. - No 1. - S. 96-107.
Svetaskov A.A., Kuprianov N.A. Primenenie energeticeskogo metoda k opredeleniu effektivnyh po vremeni modulej linejnoj vazkouprugosti // Fiz. mezomeh. - 2010. - T. 13, No 3. - S. 69-73.
Kristensen R. Vvedenie v mehaniku kompozitov. - M.: Mir, 1982. - 334 s.
Svetaskov A.A., Kuprianov N.A. Ocenka pogresnosti rascetov naprazenno-deformirovannogo sostoania linejno-vazkouprugih tel s effektivnymi po vremeni modulami // Fiz. mezomeh. - 2011. - T. 14, No 1 - S. 101-106.
Rekac V.G. Rukovodstvo k reseniu zadac po teorii uprugosti. - M.: Vyssaa skola, 1966. - 229 s.
Bugakov I.I. Polzucest’ polimernyh materialov (teoria i prilozenia). - M.: Nauka, 1973. - 288 s.
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