Stress-Strain Analysis of the Circular Orthotropic Plate Under Circumferential Loading

Abstract

AbstractThe aim of this work is to construct and analyze the resulting solutions for a circular orthotropic plate using analytical methods that allow integrating differential equations containing discontinuous functions. Discontinuous functions are understood here as a unit function, a delta function and its derivatives. This approach makes it possible to directly integrate the differential equations of plates with discontinuous load and stiffness characteristics. This eliminates the need to cut the plate into separate elements, each of which has continuous load and stiffness characteristics. The article shows how the resolving differential equation of a circular orthotropic plate is obtained from the equilibrium equations. The case of an annular load acting on an orthotropic plate is considered and a comparison with the results obtained for an isotropic plate is made. It is concluded that the bending moments at α2 < 1, that is, for the plates with radial stiffness D1 greater than circumferential stiffness D2, at the center, the plates turn to infinity, but at the same time, at α2 > 1, that is, in the case when D2 > D1, bending moments vanish. Both that and the other results do not correspond to the conditions of orthotropic plates’ real work. This means that for orthotropic circular plates, Kirchhoff hypotheses are not applicable at the point r = 0. The article gives recommendations on the calculation of circular plates under the action of a load distributed over a circle, as well as reinforced by several circumferential ribs, which are introduced into the original differential equations by delta functions.KeywordsCircular plateOrthotropic materialDeflectionBending momentsDiscontinuous functionsUnit functionDelta functionDifferential equationsIntegrationAxially-symmetric deformations