Abstract
The processes of deformation of some of the widely used layered composite materials with elastomeric matrix, consisting of thin unidirectionally reinforced layers, or from alternating unidirectionally reinforced and isotropic layers are considered.The method of solving the problems of thermoelasticity of constructions from such materials is proposed, which is based on the finite element method.To form of resolving equalizations of finite element method for layered solid with initial tensions the super element method is considered. For every layer of finite element the stiffness matrix is built on the basis of incremental theory of deformation.The decision of task for the package of finite elements, that modeling the package of the layered construction, is taken to the decision of the system of equalizations in relation to moving of knots to the surfaces of package.On the second stage of decision of task moving of knots is calculated to the border of division of layers.The components of tensor of tensions are calculated for every layer taking into account the temperature of layer.The field of temperatures determined for all package on the basis decisions of task of heat conductivity.At the construction of matrix of heat conductivity an ideal thermal contact is assumed between layers.The function of internal heat source is calculated for every layer as average energy for the complete cycle of loading.The solution of the linked problem of thermoelasticity of a layered composite is obtained by the method of successive approximations.The offered method is applied for the decision of task about thermoelasticity deformation and dissipative warming-up of pneumatic tires. Pressure in a tire is considered as an initial load.Loading is attached to the axis of wheel creates additional deformations of tire. The process of tire roll is considered as cyclic deformation.Solution of the linked task of thermoelasticity is offered for over a large size tireDependences of temperature of dissipative warming up are got on frequency of vibrations and size of loading.The got results satisfactorily comport with experimental data.
Highlights
В роботі розглянуто суперелементний підхід до формування розрахункових рівнянь метода скінченних елементів для шаруватих конструкцій
Постановка задачі та її розв'язання
/ Киричевский В.В., Дохняк Б.М., Козуб Ю.Г., Гоменюк С.И., Киричевский Р.В., Гребенюк С.Н./ – К.: Наукова думка, 2005
Summary
В роботі розглянуто суперелементний підхід до формування розрахункових рівнянь метода скінченних елементів для шаруватих конструкцій. Роботи [1,2,3,4,5,6, 8,9,10,11,12,13, 16,17,18,19, 23] присвячено дослідженню пружних характеристик шаруватих композитів, зокрема, гумокордного матеріалу та створенню математичних моделей на основі методу скінченних елементів для дослідження напружено-деформованого стану конструкцій із гумокордних матеріалів [7, 9, 11, 12]. Проте при визначенні ефективних пружних характеристик гумокордного матеріалу поздовжній та поперечний модулі пружності корду вважалися рівними, що не для всіх матеріалів виконується і відповідно, обмежує застосування наведених співвідношень.
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