Abstract

In this article, we present a refined mathematical model of the stress–strain state of multilayer composite cylindrical shells taking into account the piezoelectric effect. The displacements and the electric potential of the shell are represented as polynomials in the normal coordinates two degrees higher in comparison with the classical Kirchhoff–Love type of theory. A mathematical model of the electromechanical state of composite shells is obtained using the variational Lagrange principle. The formulated electroelasticity boundary value problem is solved by reducing three-dimensional equations to two-dimensional ones. An example of calculating the stress state of the boundary layer type of composite cylindrical shells with symmetric and asymmetric distributions of layers under the action of arbitrary mechanical and electrical loads is treated taking into account the piezoelectric effect.

中文翻译：

---

基于精细理论的复合圆柱壳应力状态考虑压电效应

摘要

在本文中，我们提出了考虑压电效应的多层复合圆柱壳应力应变状态的精确数学模型。与经典的 Kirchhoff-Love 类型的理论相比，壳的位移和电势在法线坐标中表示为多项式，该多项式高出两度。利用变分拉格朗日原理获得了复合壳机电状态的数学模型。公式化的电弹性边值问题通过将三维方程简化为二维方程来求解。