Ітераційні алгоритми розв’язання плоскої задачі для середовища з суттєвим проявом внутрішнього тертя
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Дата
2022
Автори
Багрій, О.В.
Bahrii, Olena
Назва журналу
Номер ISSN
Назва тому
Видавець
Хмельницький національний університет
Анотація
Розглядається обґрунтування ітераційного алгоритму чисельного розв’язання плоскої фізично нелінійної
граничної задачі механіки дискретного середовища. Особливістю задачі є урахування впливу на деформування
середовища внутрішнього кулонового тертя.
The purpose of research is to develop an algorithm for solving of a flat nonlinear problem of mechanics of discrete environment, which laws of deformation of take into account the effect of the internal friction. Described the explanation of the iterative algorithm for the numerical solution of the plane physically nonlinear boundary value problems of mechanics of discrete environment. Feature of the problem is the consideration of the effect of internal Coulomb friction on the deformation of the environment. When solving the problem in displacements for finite simplex elements, the continuity conditions are always satisfied at the nodes and at the faces of the element. Solving the system of canonical linear equations of the displacement method ensures the fulfillment of the equilibrium conditions in each node of the discrete computational domain. Therefore, the calculation procedure is organized in such a way that the obtained solutions also comply with the laws of deformation of the material. Known iterative methods of variable stiffness, initial stresses or initial deformations, which differ only in the method of obtaining solutions, can be used for this purpose. The analysis showed that the most effective method for solving the formulated physically nonlinear problem is the variable stiffness, on the basis of which the iterative algorithm was developed. Described in the article iterative algorithm for solving of a flat boundary value problems of mechanics of a discrete environment allows to take into account the influence on the process of deformation internal friction. It can also be used to solve problems in the mechanics of solid deformable body with a most influence of internal friction, thermo-elasticity problems, etc.
The purpose of research is to develop an algorithm for solving of a flat nonlinear problem of mechanics of discrete environment, which laws of deformation of take into account the effect of the internal friction. Described the explanation of the iterative algorithm for the numerical solution of the plane physically nonlinear boundary value problems of mechanics of discrete environment. Feature of the problem is the consideration of the effect of internal Coulomb friction on the deformation of the environment. When solving the problem in displacements for finite simplex elements, the continuity conditions are always satisfied at the nodes and at the faces of the element. Solving the system of canonical linear equations of the displacement method ensures the fulfillment of the equilibrium conditions in each node of the discrete computational domain. Therefore, the calculation procedure is organized in such a way that the obtained solutions also comply with the laws of deformation of the material. Known iterative methods of variable stiffness, initial stresses or initial deformations, which differ only in the method of obtaining solutions, can be used for this purpose. The analysis showed that the most effective method for solving the formulated physically nonlinear problem is the variable stiffness, on the basis of which the iterative algorithm was developed. Described in the article iterative algorithm for solving of a flat boundary value problems of mechanics of a discrete environment allows to take into account the influence on the process of deformation internal friction. It can also be used to solve problems in the mechanics of solid deformable body with a most influence of internal friction, thermo-elasticity problems, etc.
Опис
Ключові слова
ітераційний алгоритм, внутрішнє тертя, дискретне середовище, iterative algorithm, discrete environment, internal friction
Бібліографічний опис
Багрій О. В. Ітераційні алгоритми розв’язання плоскої задачі для середовища з суттєвим проявом внутрішнього тертя / О. В. Багрій // Вісник Хмельницького національного університету. Технічні науки. - 2022. - № 4. - С. 42-45.