Open AccessInfluence of Boundary Conditions on the Stress-Strain State of a Corrugated Sheet Under Its Weight
Author(s) -
Alexey N. Beskopylny,
Elena Kadomtseva,
Grigory Strelnikov,
Yaroslav Shabanov
Publication year - 2019
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/661/1/012029
Subject(s) - orthotropic material , perpendicular , legendre polynomials , deflection (physics) , boundary value problem , stiffness , amplitude , bending moment , galerkin method , geometry , stress (linguistics) , stress functions , mathematical analysis , mathematics , structural engineering , materials science , mechanics , physics , classical mechanics , optics , composite material , engineering , finite element method , linguistics , philosophy
In this paper, the calculation of the corrugated sheet is reduced to the calculation of the strength and stiffness of the corrugated plate under its weight. The plate is made structurally orthotropic with different cylindrical stiffnesses in two mutually orthogonal directions. The curved middle surface is described by a fourth-order differential equation and is solved by the Bubnov-Galerkin method. As approximating functions in the expansion of the deflection, beam functions are also used to compare the Legendre function. It is shown that the beam functions give much worse convergence than the Legendre functions. The influence of the location of the rigid and hinged support, located in the direction of the guided line of the wave and perpendicular to it, was investigated. Rigid attachment along the side coinciding with the guiding wave reduces the deflections and the bending moments. The stress-strain state of a wavy and flat plate is compared with the same mechanical and geometric characteristics. The influence of the amplitude of the wave amplitude on the stress-strain state of a wavy plate is analyzed. It is shown that an increase in the wave amplitude leads to an increase in the strength and stiffness of a wavy plate.