Calculation of the three-layer plate, lying on the vinkler’s base by a variation-heterogeneous method
V. F. Muschanov, A. I. Demidov
Donbas National Academy of Civil Engineering and Architecture
Annotation: The article is devoted to variational and heterogeneous application method of calculation of the rectangular three-layer plates on the resilient base taking into account the displacement between its layers on the ground of variational equation. Lagrange the linear dependence is assumed between bending and rebuff of the resilient basement on Vinkler. While recording of Lagrange the variational equation of the connection between tensions and deformations is represented in form of the Hook’s law, but taking into account the displasement between the layers of the plate. Geometrical equations are accepted in the linear in setting the form Koshy correlations. The material of each layer of the plate has the different modules of resiliency of Еі (i = 1, 2, 3), but similar coefficient of Puasson. Kinematic boundary conditions are satisfied exactly, but static – on the free from fixing of the plate edge approximately. Two examples of calculation of the three-layer plate are considered. The first example is the rectangular scale-board, hardly jammed along the whole contour. The example is the plate calculation fixed with the hinges along the contour and loosened with the rectangular opening, edges of which are free from fixing. Both plates are under the normal distributed loading. Solving tasks similarity is checked up by means of condensing of the net. The fields of bending of ware represented, bending moments of Мх, and profiles of normal tensions σx on the thickness of the plate in the most loaded sections. Work is devoted to the actual question of structural mechanics of the three-layer plates, lying on the continuous resilient base loosened with large cuts.
Keywords: the rectangular three-layer plate with the opening, variantion and heterogeneous method, various operator.
Pages: 77-91.
Link for citation: Muschanov, V. F.; Demidov, A. I. Calculation of the three-layer plate, lying on the vinkler’s base by a variation-heterogeneous method. – Text : electronic. – In: Modern Industrial and Civil Construction. – 2010. – Vol. 6, N 2. – Р. 77-91. – URL: https://donnasa.ru/publish_house/journals/spgs/2010-2/03_muschanov_demidov.pdf (date of access: 16.09.2024). (in Russian)
Vol. 6, N 2 (2010)Journal: Modern Industrial and Civil Construction
Publish house: Donbas National Academy of Civil Engineering and Architecture