Abstract

In this article, on the basis of a refined theory, we study the stress state of a conical shell of the “boundary layer” type. In comparison with the classical theory, the sought displacements of the shell are approximated by polynomials along the coordinate normal to the median surface with a degree two units higher. Based on the equations of the three-dimensional elasticity theory and the Lagrange variational principle, a system of differential equations of equilibrium in displacements with variable coefficients is obtained. The solution of the formulated boundary value problem is carried out by using the methods of finite differences and matrix sweep. The results can be used when assessing the strength and durability of shell structures.

中文翻译：

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基于精细理论的圆锥壳边界区域应力状态

摘要

在本文中，基于改进的理论，我们研究了“边界层”类型的圆锥形壳体的应力状态。与经典理论相比，壳的寻找位移是通过多项式沿垂直于中间曲面的坐标近似的，其度数高了两个单位。基于三维弹性理论方程和拉格朗日变分原理，得到了变系数位移平衡方程的微分方程组。用有限差分法和矩阵扫描法求解所提出的边值问题。该结果可用于评估壳体结构的强度和耐久性。