Застосування ІТ технологій в механіці деформованого твердого тіла
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Дата
2017
Автори
Рудницький, В.Б.
Ярецька, Н.О.
Венгер, В.О.
Rudnickij, V.B.
Yarets'ka, N.O.
Venger, V.О.
Назва журналу
Номер ISSN
Назва тому
Видавець
Хмельницький національний університет
Анотація
У статті з використанням співвідношень лінеаризованої теорії пружності представлено розв’язок контакт
ної задачі про контактну взаємодію пружного шару з початковими напруженнями і співвісних попередньо напруже-
них циліндрів із застосуванням ІТ технологій. Розроблено алгоритм та комп’ютерна програма числового обчислення
компонентів напружено-деформованого стану контактуючих тіл з початковими напруженнями при довільній струк-
турі пружного потенціалу.
The article is devoted to the research of two problems of contact interaction of prestressed bodies, namely: 1) the pressure of an elastic cylinder die upon an elastic layer and foundation with initial (residual) stresses; 2) contact interaction of elastic layer with initial stresses and prestressed coaxial cylinders with using the IT technologies. The authors developed a computer program and algorithm of numerical calculation components deflected mode of contacting bodies with initial stresses. In general, the research was carried out for the theory of great initial (ultimate) and two variants of the theory of small initial deformations within the framework of linearized theory of elasticity with the elastic potential having arbitrary structure. It is assumed that elastic potentials are two continuously differentiated functions of algebraic invariants of the Green tensor deformation (the initial states of the layer, of the cylindrical punch and of the foundation remains uniform and equal). Was used method of solving the dual integral equations. These equations are reduced to Fredholm integral equation of the second kind. Solution of integral equations was found by a method of successive approximations. The problem was reduced to solving an infinite system of algebraic equations. The system was solved by numerical methods (by reduction) and software tools.
The article is devoted to the research of two problems of contact interaction of prestressed bodies, namely: 1) the pressure of an elastic cylinder die upon an elastic layer and foundation with initial (residual) stresses; 2) contact interaction of elastic layer with initial stresses and prestressed coaxial cylinders with using the IT technologies. The authors developed a computer program and algorithm of numerical calculation components deflected mode of contacting bodies with initial stresses. In general, the research was carried out for the theory of great initial (ultimate) and two variants of the theory of small initial deformations within the framework of linearized theory of elasticity with the elastic potential having arbitrary structure. It is assumed that elastic potentials are two continuously differentiated functions of algebraic invariants of the Green tensor deformation (the initial states of the layer, of the cylindrical punch and of the foundation remains uniform and equal). Was used method of solving the dual integral equations. These equations are reduced to Fredholm integral equation of the second kind. Solution of integral equations was found by a method of successive approximations. The problem was reduced to solving an infinite system of algebraic equations. The system was solved by numerical methods (by reduction) and software tools.
Опис
Ключові слова
ІТ технології, лінеаризована теорія пружності, початкові (залишкові) напруження, інте- гральне рівняння Фредгольма, метод послідовних наближень, IT technologies, linearized theory of elasticity, initial (residual) stress, Fredholm integral equations, the method of consecutive approximations
Бібліографічний опис
Рудницький, В.Б. Застосування ІТ технологій в механіці деформованого твердого тіла [Текст] / В. Б. Рудницький, Н. О. Ярецька, В. О. Венгер // Проблеми трибології. – 2017. – № 2. – С. 22-30.