Чисельно-аналітичне дослідження ортотропної в’язкопружності склопластику на прикладі ремонтної накладки магістрального трубопроводу
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Дата
2014
ORCID
DOI
Науковий ступінь
Рівень дисертації
Шифр та назва спеціальності
Рада захисту
Установа захисту
Науковий керівник
Члени комітету
Видавець
НТУ "ХПІ"
Анотація
Описано чисельно-аналітичні дослідження напружено-деформованого стану ділянки трубопроводу з в’язкопружною ремонтною накладкою в плоскій постановці. Розроблено математичну модель ортотропної в’язкопружності. З метою розв’язання математичної моделі запропоно-
вано метод, заснований на використанні квадратурних формул для приблизного обчислення
інтегралів та аналітичному вирішенні неоднорідних диференційних рівнянь. Результати розрахунків представлено у вигляді графіків розподілу переміщень та напружень за радіусом та у часі. Зроблено висновок щодо доцільності врахування ортотропії в’язкопружних властивостей матеріалу при вирішенні задачі в’язкопружності.
In this paper a numerical-analytical study on a stress-strain state of a steel pipeline section with a repair fiberglass viscoelastic layer is described. The layer is considered long enough that allows to solve the problem in a flat axisymmetric statement. A mathematical model of viscoelastic behavior of a fiberglass is proposed, moreover this model allows to simulate an order of anisotropy of viscoelastic properties that exceeds an order of anisotropy of elastic ones. To mirror viscoelastic behavior of the construction more correctly an orthotropical viscoelasticity is used in the mathematical model. As a result of transformation of the original system of equations of elasticity theory it becomes necessary to solve the inhomogeneous integral equation. In order to solve it quadrature formulas are used. With help of them an iteration process in time was built where an inhomogeneous differential equation with viscoelastic prehistory in right side was solved. For determining values of integration constants of differential equations boundary conditions are rearranged using quadrature formulas. For the case of definite values of physical and geometrical parameters of the construction the right rectangle formula was chosen. To evaluate an error of the mathematical model a discrepancy between the analytical results form previous research and the results according to the given model for the simplified isotropic set of viscoelastic parameters was estimated. It is shown that for 500 iterations the discrepancy is less than 0.1% that allows to use this values for further calculations. Calculation results for the case of orthotropic viscolasticity are presented as displacement and stress distributions versus time curves. Also a comparison between this results and the stress strain state of the construction in case of isotropic viscoelasticity was made. It is shown that even for a slight deviation of viscoelastic model from isotropic to orthotropic a change of the main parameters of the stress strain state is approximately 20% considering their time varying parts. Based on this fact a conclusion about a necessity of using the analytical model of orthtropic viscoelasticity in calculation or, at least, evaluation of the stress strain state of constructions with viscoelastic parts was made. Also built numerical-analytical model allows to disseminate the results on cases of more complex geometrical and physical conditions without changing in a main idea of the method.
In this paper a numerical-analytical study on a stress-strain state of a steel pipeline section with a repair fiberglass viscoelastic layer is described. The layer is considered long enough that allows to solve the problem in a flat axisymmetric statement. A mathematical model of viscoelastic behavior of a fiberglass is proposed, moreover this model allows to simulate an order of anisotropy of viscoelastic properties that exceeds an order of anisotropy of elastic ones. To mirror viscoelastic behavior of the construction more correctly an orthotropical viscoelasticity is used in the mathematical model. As a result of transformation of the original system of equations of elasticity theory it becomes necessary to solve the inhomogeneous integral equation. In order to solve it quadrature formulas are used. With help of them an iteration process in time was built where an inhomogeneous differential equation with viscoelastic prehistory in right side was solved. For determining values of integration constants of differential equations boundary conditions are rearranged using quadrature formulas. For the case of definite values of physical and geometrical parameters of the construction the right rectangle formula was chosen. To evaluate an error of the mathematical model a discrepancy between the analytical results form previous research and the results according to the given model for the simplified isotropic set of viscoelastic parameters was estimated. It is shown that for 500 iterations the discrepancy is less than 0.1% that allows to use this values for further calculations. Calculation results for the case of orthotropic viscolasticity are presented as displacement and stress distributions versus time curves. Also a comparison between this results and the stress strain state of the construction in case of isotropic viscoelasticity was made. It is shown that even for a slight deviation of viscoelastic model from isotropic to orthotropic a change of the main parameters of the stress strain state is approximately 20% considering their time varying parts. Based on this fact a conclusion about a necessity of using the analytical model of orthtropic viscoelasticity in calculation or, at least, evaluation of the stress strain state of constructions with viscoelastic parts was made. Also built numerical-analytical model allows to disseminate the results on cases of more complex geometrical and physical conditions without changing in a main idea of the method.
Опис
Ключові слова
природний газ, ремонтний бандаж, концентратори напружень, математична модель, квадратурні формули, repair layer, orthotropic viscoelasticity, integral equation, quadrature formula
Бібліографічний опис
Львов Г. I. Чисельно-аналітичне дослідження ортотропної в’язкопружності склопластику на прикладі ремонтної накладки магістрального трубопроводу / Г. I. Львов, В. Г. Мартиненко // Вісник Нац. техн. ун-ту "ХПІ" : зб. наук. пр. Темат. вип. : Динаміка і міцність машин. – Харків : НТУ "ХПІ". – 2014. – № 58 (1100). – С. 68-77.