Journal of Samara State Technical University, Ser. Physical and Mathematical SciencesJournal of Samara State Technical University, Ser. Physical and Mathematical Sciences1991-86152310-7081Samara State Technical University6086810.14498/vsgtu1772Research ArticleThe steady-state creep of long membrane in a rigid matrix at a variable transverse pressureLokoshchenkoAlexander MikhaylovichDoctor of physico-mathematical sciences, Professorloko@imec.msu.ruTeraudWalentin ViktorovichCandidate of technical sciencesShevarovaEkaterina Alekseevnakat121193@ya.ruLomonosov Moscow State University, Institute of MechanicsSamara State Technical UniversityMoscow Aviation Institute (State Technical University)0110202024344546814022021Copyright © 2020, Samara State Technical University2020The problem of the steady-state creep of a long rectangular membrane in constrained conditions inside a rigid matrix is investigated with a piecewise constant dependence of the transverse pressure $q$ on time $t$. The problem considers a long matrix of rectangular cross section, in which the ratio of its height to width is not less than 0.5. As an example, the creep of the membrane is investigated with a single change in the magnitude of the transverse pressure over time. Three variants of the contact conditions of the membrane and the matrix are considered: perfect sliding, adhesion and sliding taking friction into account. In this paper, four stages of membrane deformation were investigated. At the first stage (elastic deformation), the membrane, flat in the initial state, under the action of pressure, instantaneously is deformed elastically, acquiring the form of an open circular cylindrical shell with a central angle $2\alpha _1 $. At the second stage, the membrane is deformed under steady-state creep conditions up to the moment when the side walls of the matrix touch. The third stage ends when the membrane touches the transverse wall of the matrix. In the fourth stage, the membrane is in contact with the matrix on the transverse and lateral sides. The analysis is carried out until the time of almost complete adherence of the membrane to the matrix, at which the ratio of the radius of the membrane near the corners of the matrix to the initial width of the membrane is 0.005. For the third and fourth stages, the friction force of the membrane on the matrix walls is additionally taken into account. The dependences of the thickness of various parts of the membrane on time and on the intensity of stresses in the membrane on time are obtained. In relation to this formulation of the problem, deviations from the rule of summing the partial times of filling the matrix are considered.membranesteady-state creepthe matrixtransverse pressureideal slidingadhesionnon-stationary loadingfrictionмембранаустановившаяся ползучестьматрицапоперечное давлениеидеальное скольжениеприлипаниенестационарное нагружениетрение[Odqvist F. K. G., Mathematical Theory of Creep and Creep Rupture, Clarendon Press, Oxford, 1966, ix+168 pp.][Качанов Л. М., Основы механики разрушения, Наука, М., 1974, 312 с.][Малинин Н. Н., Ползучесть в обработке металлов, Машиностроение, М., 1986, 216 с.][Локощенко А. М., Ползучесть и длительная прочность металлов, М., Физматлит, 2016, 504 с.][Локощенко А. М., Терауд В. В., "Ползучесть длинной узкой мембраны в стесненных условиях вплоть до разрушения", ПМТФ, 54:3 (2013), 126-133][Демин В. А., Локощенко А. М., Жеребцов А. А., "Ползучесть длинной прямоугольной мембраны внутри криволинейной матрицы", Изв. вузов. Машиностроение, 1998, № 4-6, 41-46][Шестериков С. А., Юмашева М. А., "Конкретизация уравнения состояния в теории ползучести", Изв. АН СССР. МТТ, 1984, № 1, 86-91][Локощенко А. М., Абросимова Е. А., "Установившаяся ползучесть длинной мембраны внутри жесткой матрицы при кусочно-постоянной зависимости скорости изменения поперечного давления от времени", ПМТФ, 60:1 (2019), 103-113][Robinson E. L., "Effect of temperature variation on the long time rupture strength of steels", Trans. Am. Soc. Mech. Engrs, 74:5 (1952), 777-780][Гуляев В. Н., Колесниченко М. Г., "К оценке долговечности в процессе ползучести при ступенчатом изменении нагрузки", Завод. лаб., 1963, № 6, 748-752][Marriott D. L., Penny R. K., "Strain accumulation and rupture during creep under variable uniaxial tensile loading1", J. Strain Analysis, 8:3 (1973), 151-159][Осасюк В. В., Олисов А. Н., "К вопросу о гипотезах суммирования относительных долговечностей", Пробл. прочн., 1979, № 11, 31-33]