STRESSED STATE IN EDGE ZONE OF CYLINDRICAL SHELLS BASED ON A NON-CLASSIC THEORY WITH THE PIEZOELECTRIC EFFECT

Abstract

Based on the refined theory in this paper presents the stress-strain state of cylindrical shells taking into account the piezoelectric effect. The mechanical displacements and electrical potentials of the shell are approximated by polynomials in the normal coordinate two degrees higher in relation to the classical theory of the Kirchhoff-Love type. The equations of the theory of elasticity and the laws of electrostatics are used to obtain model of electroelasticity behavior. By using Lagrange variational principle a system of differential equations of equilibrium in displacements and potentials with boundary conditions is derived. Trigonometric Fourier series in the circumferential coordinate is used to reduce partial differential equations system to ordinary differential equations. The formulated boundary value problem of the electroelastic state of the shell is solved by an operator method based on the Laplace transform. Transverse normal and tangential stresses of the linear equilibrium equation of the three-dimensional theory of elasticity. Examples of calculating the stress state of a cylindrical piezoelectric shell with clamped support are provided. Two cases are analyzed: the shell is under the influence of mechanical loads and electrical potentials. A comparison of the results obtained according to the proposed theory and the classical theory is carried out. It has been established that there is an additional stress state of the "boundary layer" type. It allows to confirm the practical value of the developed mathematical model and a significant contribution to the general stress-strain state with the strength and durability of cylindrical shells modeled elements of mechanical engineering structures taking into account the piezoelectric effect.