Аналітичне дослідження контактної поведінки ділянки трубопроводу з в'язкопружною ремонтною накладкою

Abstract

У статті описано аналітичні дослідження напружено-деформованого стану ділянки трубопроводу з в’язкопружною ремонтною накладкою в плоскій постановці. Побудована крайова задача для інтегро-диференційних рівнянь та запропоновано метод її вирішення. Результати розрахунків представлено у вигляді графіків розподілу переміщень та напружень за радіусом та у часі. Зроблено висновок щодо впливу в’язкопружності на загальну оцінку міцності конструкції.

In this paper an 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. The analytical model including accounting of an isotropic viscoelasticity involves the need to construct and solve the boundary value problem for a system of integro-differential equations. In order to do it anapproach based on a method of differentiation of integral equations is proposed. It is shown that for the initial time moment a solution of viscoelastic problem coincides with an elastic solution. Calculation results are presented as displacement and stress distributions versus radius and time curves. The viscoelastic model lets detect and discover such important properties of viscoelasticity asan increase of displacement over time and a stress relaxation in the composite layer. It is observed that at the same time the stress relaxation in the layer causes an increase of dangerous circumferential stresses in the steel pipeline. According to these results a conclusion about an impact of viscoelasticity on an overall assessment of strength of the construction is made. Also it is shown that for the specific set of physical and geometrical parameters of the construction stress relaxation in layer occurs in the moment of time with a value 200 hours and the maximum circumferential stress value increases by seven percent. The time result coincide with relaxation time obtained using numerical model based on a finite-element method of a commercial computeraided engineering complex. The stress increase result also responds to the numerical assessment and this value can be much higher in case of stress concentration due to presence of defects in pipeline walls. Proposed analytical model allows to save computational resources and to extend its application to more complex cases of the stress-strain state.