Abstract

The use of effective approximations that increase the rate of convergence of numerical results when constructing a finite element model of bearing layers for a more accurate layer-by-layer analysis of the stress-strain state of three-layer irregular cylindrical shells is considered. It is believed that the carrier layers are sufficiently thin and rigid, and two-dimensional finite elements of natural curvature, constructed on the basis of the classical theory of moment shells, are used to simulate the stress-strain state. It is assumed that the aggregate layer can be modeled in thickness by the required number of three-dimensional finite elements, which allows one to take into account the change in geometric and physical-mechanical characteristics, as well as the parameters of the stress-strain state, not only along the meridional and circumferential coordinates, but also along the thickness of the shell and the aggregate layer. The finite element approximations considered allow one to reduce the order of systems of equations, i.e. to reduce the dimensionality of the problems being solved in comparison with the traditionally used approximations, which is especially important for layer-by-layer analysis of layered-heterogeneous structures. The high convergence rate of the numerical results obtained using the considered finite element model of the bearing layers is confirmed by a comparison with other known finite elements.

中文翻译：

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三层圆柱状不规则旋转壳体应力-应变状态逐层分析的有效承载层模型

摘要

在构建轴承层的有限元模型时，考虑使用有效的近似方法提高数值结果的收敛速度，以便对三层不规则圆柱壳的应力-应变状态进行更精确的逐层分析。据信载体层足够薄且刚性，并且基于矩矩壳的经典理论构造的自然曲率的二维有限元用于模拟应力-应变状态。假定可以通过所需数量的三维有限元来对聚集层的厚度进行建模，这使人们可以考虑几何和物理机械特性的变化以及应力应变的参数州，不仅沿子午线和圆周坐标，而且沿壳和骨料层的厚度。所考虑的有限元近似值使人们可以减少方程组的阶数，即与传统使用的近似值相比，可以减少要解决的问题的维数，这对于分层异质结构的逐层分析尤为重要。通过与其他已知的有限元进行比较，可以确定使用考虑的轴承层有限元模型获得的数值结果的高收敛速度。与传统上使用的近似方法相比，可以减少要解决的问题的维数，这对于层状异质结构的逐层分析尤为重要。通过与其他已知的有限元进行比较，可以确定使用考虑的轴承层有限元模型获得的数值结果的高收敛速度。与传统上使用的近似方法相比，可以减少要解决的问题的维数，这对于层状异质结构的逐层分析尤为重要。通过与其他已知的有限元进行比较，可以确定使用考虑的轴承层有限元模型获得的数值结果的高收敛速度。