КРАЕВОЕ НАПРЯЖЕННО-ДЕФОРМИРОВАННОЕ СОСТОЯНИЕ КРУГЛОЙ ПЛАСТИНЫ ПЕРЕМЕННОЙ ТОЛЩИНЫ НА ОСНОВЕ НЕКЛАССИЧЕСКОЙ ТЕОРИИ

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A variant of the refined theory on calculation of the stress-strain state of circular plates with symmetrically various thicknesses according to an arbitrary law in the radial direction was presented. Equations of the plate state were established by using the three-dimensional elasticity theory. The required displacements were approximately calculated according to upright direction to the middle plane by polynomials with two degrees higher than in the classical Kirchhoff - Love theory. The differential equation at equilibrium in displacements with various coefficients was obtained by using means of the Lagrange variational principle. The direct integration of the equilibrium equations in the three-dimensional elasticity theory was used to determine the transverse normal and shear stresses. Of an isotropic circular plate with changing in thickness by using the analyzing Fourier chain, the obtained differential equilibrium equations in displacements with variable coefficients containing supplement components and taking into account of the effect of thickness on the stress-strain state of the plate. Examples of calculating the stress state of a circular plate with a thickness varying according to linear and parabolic laws under the action of a uniformly distributed load were considered. The limited difference method was employed to solve the boundary value problem. Comparison results of the refined and classical theories were investigated. It is demonstrated that the study on the stress state in the zones of its distortion (compounds, local loading zones, etc.) should use a refined theory, since the additional corresponding stresses of the “boundary layer” type are of the same order with the values of the main (internal) stress state. This is important to increase the reliability of strength calculations of such elements of aircraft-rocket structures as the power housings of aircraft, their various transition zones and connections, as well as objects in various engineering industries.