On the flexure of thin cylindrical shells and other "thin" sections
On the flexure of thin cylindrical shells and other "thin" sections
复制标题
DOI：
10.1098/rspa.1927.0125
复制
发表时间：
1927-09-01
期刊：
影响因子：
--
通讯作者：
Brazier, LG
中科院分区：
文献类型：
--
作者：
Brazier, LG
从圣维南挠曲问题的解中得到的一个普遍认可的推论是，在材料的经济性方面，将材料布置在离中性轴一定距离的梁优于实心截面。然而，St. Yenant的解决方案表明，随着材料厚度的减少和与中性轴的距离的增加，这种优势会无限制地增加。当然，人们普遍意识到，这一结论不受普通工程实践的支持，最近在高强度钢的使用和飞机结构问题方面的经验强调了进一步研究挠度问题的必要性。当各向同性弹性固体的平衡方程通过忽略高于第一阶的项而成为线性时，得到St. Venant解，并且根据Kirchhoff的确定性定理，这些解可以被认为是唯一的和稳定的。正如r.v. Southwell在他的《弹性稳定性的一般理论》中所指出的那样，为了解决稳定性问题，有必要包括一些二阶效应。事实上，只有当这些变得相当大时，基尔霍夫定理才会失效，不稳定性才会成为可能。通过这种一般处理方法，可以得到或指出各种类型的不稳定性，但只有那些易于分析或具有实际意义的不稳定性（由于“弹性极限”是所有实际材料的特征）是那些在不稳定时刻应变仍然很小的不稳定性。布莱恩特已经证明，只有当身体的一个维度比其他维度小时，这种情况才会发生，就像在薄杆和壳的情况下一样。
It is a generally appreciated deduction from St. Venant’s solution of the flexure problem that a beam in which the material is disposed at a distance from the neutral axis is superior to the solid section in economy of material. St. Yenant’s solution, however, suggests that this advantage increases without limit as the thickness of the material is reduced and the distance from the neutral axis is increased. It has, of course, been generally realised that this conclusion is not supported by ordinary engineering practice, and recent experience in the use of high tensile steels and problems of aircraft structure have emphasised the desirability of a further examination of the flexure problem. St. Venant’s solutions are obtained when the equations of equilibrium of an isotropic elastic solid are made linear by the neglect of terms of higher orders than the first: and by Kirchhoff’s theorem of determinancy these solutions may then be considered unique and stable. To attack problems of stability it is necessary, as is shown by R. V. Southwell in his ‘General Theory of Elastic Stability,’ to include some of the second order effects. It is, in fact, only when these become considerable that Kirchhoff’s theorem fails and instability becomes possible. By this general treatment various classes of instability are obtained or indicated, but the only ones susceptible to analysis or of practical interest (on account of the “elastic limit” which is a feature of all practical materials) are those in which at the moment of instability the strains are still small. Bryant has shown that this will only occur, as in the case of thin rods and shells, when one dimension of the body is small compared with others.