The objects of consideration are thin linearly elastic Kirchhoff–Love-type open circular cylindrical shells having a functionally graded macrostructure and a tolerance-periodic microstructure in circumferential direction. The first aim of this contribution is to formulate and discuss a new mathematical averaged non-asymptotic model for the analysis of selected stability problems for such shells. As a tool of modelling we shall apply the tolerance averaging technique. The second aim is to derive and discuss a new mathematical averaged asymptotic model. This model will be formulated using the consistent asymptotic modelling procedure. The starting equations are the well-known governing equations of linear Kirchhoff–Love second-order theory of thin elastic cylindrical shells. For the functionally graded shells under consideration, the starting equations have highly oscillating, non-continuous and tolerance-periodic coefficients in circumferential direction, whereas equations of the proposed models have continuous and slowly-varying coefficients. Moreover, some of coefficients of the tolerance model equations depend on a microstructure size. It will be shown that in the framework of the tolerance model not only the fundamental cell-independent, but also the new additional cell-dependent critical forces can be derived and analysed.

考虑的对象是薄的线弹性基尔霍夫-洛夫型开口圆柱壳，具有功能梯度宏观结构和圆周方向公差周期性微观结构。本贡献的首要目的是制定和讨论一种新的数学平均非渐近模型，用于分析此类壳的选定稳定性问题。作为建模工具，我们将应用公差平均技术。第二个目标是推导并讨论一种新的数学平均渐近模型。该模型将使用一致的渐近建模程序来制定。起始方程是著名的薄弹性圆柱壳线性 Kirchhoff-Love 二阶理论的控制方程。对于所考虑的功能梯度壳，起始方程在圆周方向上具有高度振荡、非连续和公差周期系数，而所提出模型的方程具有连续且缓慢变化的系数。此外，公差模型方程的一些系数取决于微观结构尺寸。将表明，在耐受模型的框架中，不仅可以导出和分析基本的细胞无关的临界力，而且还可以导出和分析新的附加的细胞依赖性临界力。