The Theory of Thin-Walled Rods of Open Profile as a Result of Asymptotic Splitting in the Problem of Deformation of a Noncircular Cylindrical Shell
The Theory of Thin-Walled Rods of Open Profile as a Result of Asymptotic Splitting in the Problem of Deformation of a Noncircular Cylindrical Shell
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DOI：
10.1007/s10659-009-9222-4
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发表时间：
2010-02
影响因子：
2
通讯作者：
Y. Vetyukov
中科院分区：
文献类型：
--
作者：
Y. Vetyukov
提出了开口薄壁杆件理论的一种新的渐近方法。对于非圆柱壳的线性静态变形问题，我们考虑了沿轴坐标缓慢变化的解。在现代壳体理论的方程中引入了一个小参数。采用了壳体应变措施的相容条件。解的级数展开式的主项由次项的可解性条件确定。我们用位移场的后续解来结束这一过程。分析表明，已知的薄壁杆件方程是渐近精确的，这些方程是用假设和位移近似的某些近似方法得到的。所给出的壳方程的半数值分析使我们能够估计所得解的精度。本文的结果为薄壁杆件理论方程的建立奠定了坚实的基础，并为截面应力分布提供了可靠的信息。
A new asymptotic approach to the theory of thin-walled rods of open profile is suggested. For the problem of linear static deformation of a noncircular cylindrical shell we consider solutions, which are slowly varying along the axial coordinate. A small parameter is introduced in the equations of the modern theory of shells. Conditions of compatibility for the shell strain measures are employed. The principal terms of the series expansion of the solution are determined from the conditions of solvability for the minor terms. We conclude the procedure with the subsequent solution for the field of displacements. The analysis shows that the known equations of thin-walled rods, which were previously obtained with some approximate methods using hypotheses and approximations of displacements, are asymptotically exact. The presented semi-numerical analysis of the shell equations allows us to estimate the accuracy of the obtained solution. The results of the paper constitute a sound basis to the equations of the theory of thin-walled rods and provide trustworthy information concerning the distribution of stresses in the cross-section.