Кусково-однорідна ортотропна пластинка з коловим розрізом, береги якого частково контактують при згині
DSpace at Ternopil State Ivan Puluj Technical University
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| Title |
Кусково-однорідна ортотропна пластинка з коловим розрізом, береги якого частково контактують при згині
Piecewise homogeneous orthotropic plate with circular cut the edges of which are partly contacting when bending |
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| Creator |
Сяський, Андрій Олексійович
Музичук, Катерина Петрівна Syasky, A. Muzychuk, K. |
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| Subject |
нескінченна ортотропна пластинка
інтегрально-диференціальні рівняння зона спаю гладкий контакт циліндричний згин напружений стан infinite orthotropic plate integral-differential equations zone of soldered joint smooth contact cylindrical bending stress state 531.3 |
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| Description |
Розглянуто задачу згину нескінченної кусково-однорідної ортотропної пластинки з коловим розрізом на лінії розділу матеріалів за умови часткового контактування його берегів. Математичну модель для цієї задачі побудовано у вигляді системи сингулярних інтегрально-диференціальних рівнянь з логарифмічними ядрами. Дослідження впливу ортотропії матеріалу пластинки на розподіл компонент напруженого стану на контурі колового отвору в пластинці і диску здійснено числовими методами механічних квадратур і колокації.
Solution of the mixed contact problem for the infinite orthotropic plate with the circular hole and the circular elastic isotropic disk which are soldered together in the part of common contour, and in the remaining contour the through cut is available between them, is introduced. Under uniformly distributed bending moments at infinity in the directions of coordinate axes and concentrated bending moments applied in the disk center, the edges of the cut contact partly on the line in the top face of the plate. Frictional forces are considered not to be available on the contact zone. The solving of the problem includes the determination of the stress state components on the contour hole of the plate, the size and the position of the contact zone. The stress state of the composite plate under of this load is presented as the superposition of the generalized two-dimensional stress state and the bending strain according to the technical theory of the bending plate. According to the statement of the problem boundary conditions in the contact zone are formulated as equality of the normal displacements of contour points on the top face of the plate and the disk. In the zone of soldered joint the perfect mechanical contact is available that is why the boundary conditions of the problem are written as equality of contact forces and contact moments and also as equality of the displacement vector components and rotation angle of normal line to the mean plane of the plate and the disk. The expressions for determination of the strain state components of the plate and the disk are presented from the contact stresses on the line of delimiting materials as integral relations with logarithmic kernels and the relations of the hoop stresses, moments and the rotational moments. Their substitution into the boundary conditions results in the system of singular integral-differential equations for finding functions, from which the contact stresses and moments are expressed. This system is enforced by power and moment conditions of equilibrium of the disk and the single-valuedness condition of flexure plate, which being combined determine the mathematical model of the problem, the exact solution of which can not be found. For its approximate solution the structure for finding functions about the ends of the contact zone and the zone of soldered joint was found. At the ends of the zone of soldered joint the contact stresses and moments are of the root feature. The finding functions are similar. In the contact zone solution of the system is chosen in the class of functions limited at its ends. The approximate solution of the problem was built by the method of mechanical quadrature and collocation. For an infinite orthotropic plate with circular cut, the edges of which partly contact under the unilateral bending at infinity, the influence of material orthotropy of the plate and the size of the zone of soldered joint on the distribution of the force and moment stresses on the line of delimiting materials of the plate and the disk was investigated. The research was conducted for five different orthotropic materials. The results of numerical calculation of the stress state components are illustrated on the graphs. The size and the position of the contact zone are determined by the method of dichotomy. The results of its calculation for different materials are presented in the table. |
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| Date |
2012
2013-06-27T09:31:28Z 2013-06-27T09:31:28Z 2012-07-25 |
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| Type |
Article
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| Identifier |
Сяський А. Кусково-однорідна ортотропна пластинка з коловим розрізом, береги якого частково контактують при згині / Сяський А., Музичук К. // Вісник ТНТУ. — 2012. — Том 67. — № 3. — С.17-25. — (механіка та матеріалознавство).
1727-7108 http://elartu.tntu.edu.ua/handle/123456789/2375 |
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| Language |
uk
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| Rights |
© „Вісник Тернопільського національного технічного університету“
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| Coverage |
Тернопіль, Україна
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| Publisher |
Тернопільський національний технічний університет ім. Івана Пулюя
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