论文标题
轴向压缩下圆柱形壳的屈曲载荷取决于横截面曲率
The buckling load of cylindrical shells under axial compression depends on the cross-section curvature
论文作者
论文摘要
众所周知，Koiter著名的理论公式对于轴向压缩下的圆形圆柱壳的临界屈曲载荷与实验数据不一致。也就是说，尽管Koiter的公式可以预测屈曲载荷的线性依赖性$λ（h）$的壳厚度$ h $（$ h> 0 $是一个小参数），但在实验中观察到依赖性$λ（h）\ sim h^{3/2} $;即，壳的扣子扣的厚度要小得多，厚度很小。人们认为，这种理论预测失败是由对不完美现象（形状和负载）的所谓敏感性引起的。 Grabovsky和第一作者在[\ textit {j。 nonl。 Sci。，} vol。 26，ISS。 1，第83---119页，2016年2月]，在轴向圆柱形外壳下屈曲的问题中，很小的负载扭曲导致屈曲负载缩放$λ（h）\ sim h^{5/4} $，$，而形状不完美可能导致缩放$λ（h）$λ（h）$ sim \ sim h he h^h^h^h^h^h^h^h^h^h^h^h^h^h^h^h^h^h^h^h^h^h^h）在垂直压缩下的圆柱形（不一定是圆形）壳的屈曲载荷$λ（H）$取决于横截面曲线的曲率。当横截面是具有均匀正弯曲的凸曲线时，则$λ（h）\ sim h，$，当横截面曲线具有正弯曲时，除了在有限的许多点以外，然后$ c_1h^{8/5} \ leqleqλ（h）
It is known that the famous theoretical formula by Koiter for the critical buckling load of circular cylindrical shells under axial compression does not coincide with the experimental data. Namely, while Koiter's formula predicts linear dependence of the buckling load $λ(h)$ of the shell thickness $h$ ($h>0$ is a small parameter), one observes the dependence $λ(h)\sim h^{3/2}$ in experiments; i.e., the shell buckles at much smaller loads for small thickness. This theoretical prediction failure is believed to be caused by the so-called sensitivity to imperfections phenomenon (both, shape and load). Grabovsky and the first author have rigorously proven in [\textit{J. Nonl. Sci.,} Vol. 26, Iss. 1, pp. 83--119, Feb. 2016], that in the problem of circular cylindrical shells buckling under axial compression, a small load twist leads to the buckling load scaling $λ(h)\sim h^{5/4},$ while shape imperfections are likely to result in the scaling $λ(h)\sim h^{3/2}.$ In this work we prove, that in fact the buckling load $λ(h)$ of cylindrical (not necessarily circular) shells under vertical compression depends on the curvature of the cross section curve. When the cross section is a convex curve with uniformly positive curvature, then $λ(h)\sim h,$ and when the the cross section curve has positive curvature except at finitely many points, then $C_1h^{8/5}\leq λ(h)\leq C_2h^{3/2}$ for $h$ small thickness $h>0.$
