Аннотації
25.12.2017
На основі методу реакцій розроблена методика обчислення параметру методом зміщення підобластей в дискретних моделях методу скінчених елементів. Проведено розв’язання тестових задач. Отримані результати підтверджують ефективність методики.
На основе метода реакций разработана методика определения параметра методом смещения подобластей в дискретных моделях метода конечных элементов. Проведено решение тестовых задач. Полученные результаты подтверждают эффективность методики.
Fracture mechanics’ parameters are used when the stress-strain state in the vicinity of the crack tip being evaluated. Energy methods have been most developed in determining of the fracture mechanics parameters to date. A method of reactions has been developed in earlier works of authors that makes it possible to determine the J-integral in discrete models of the finite element method. However, the use of the J-integral is possible in the absence of voluminous forces. The case of voluminous forces caused by the action of temperature loads is the exception of it. is used as the fracture parameter in this case. A new method for calculating of the parameter is developed in this paper, based on the reaction method. The implementation of this method involves the displacement of the subregions of integration into one finite element. Approbation of the developed approach was carried out on the test problem of deformation of a rectangular plate with a central crack. The obtained results showed that under the action of both surface and voluminous forces on the plate, the values of the parameter coincide with the standard solution. Further, the developed approach was implemented for spatial problems, using discrete models of a semi-analytic finite element method. The determination of is performed in this case at separate points of the crack front for each of which separate volumes of integration and corresponding subregions are stand out. Approbation of the technique in the spatial bodies was carried out on the test problem of the bending of a prismatic body with a lateral notch. Then the developed method was tested on two test problems in the presence of volume forces caused by the action of temperature loads. The results coincided with the values of obtained by other authors with the help of the finite element software ANSYS. Thus, the method of determining of the parameter , developed on the basis of the reaction method, makes it possible to effectively evaluate the stress-strain state in bodies with cracks under the action of surface and voluminous forces.
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