Stressed state “boundary layer” in a round plate of variable thickness according to refined theory

Abstract

Based on the refined theory, the edge stress state of an isotropic round plate of variable thickness under the influence of local load was considered. In constructing the mathematical model of the plate, three-dimensional equations of the theory of elasticity and the variation Lagrange principle were used. Displacements were represented in the form of polynomials along with the coordinate normal to the middle surface, which was two degrees higher than the classical theory of the Kirchhoff – Love type. The resolving system of equations includes eleven ordinary differential equations with variable coefficients. The solution of the formulated boundary-value problem was carried out by finite difference methods and matrix sweeps. The deformations and tangential stresses of the plate were determined from the corresponding geometric and physical equations of the elasticity theory. This article has been focused on identifying the stress state of the boundary layer type near rigidly and elastically fixed edges by the round plate where the destruction of thin-walled structural elements in machinery, including aviation and space technology, takes place.

Modeling the stress-strain state of variable-thickness composite shells and plates

“…In the articles of Firsanov V.V. [8][9][10][11], the calculation of the stress-strain state for plates and shells with asymmetric variable thickness is considered, taking into account the influence of the boundary layer effect in boundary value problems. In [12], the stability of a multilayer round plates of variable thickness from nonlinear elastic material is studied.…”