悬臂矩形板在对称边界荷载下的屈曲
On Buckling of Cantilever Rectangular Plates under Symmetrical Edge Loading
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摘要: 本文用变分法对悬臂矩形板在对称边界荷载下的稳定性进行研究.我们将对在悬臂矩形板的一对相对的自由边作用有不同的对称边界荷载时,求出薄板的最小临界力.文中分别讨论了有一对集中力,均布荷载,局部均布荷载,三角形分布荷载及一对集中力偶作用之下悬臂矩形板发生屈曲时的最小临界荷载.Abstract: The stability of cantilever rectangular plates under the symmetrical edge loading will be studied in this paper by lite varialional calculus. We are going to find out the minimum critical loading for cantilever rectangular plates subjected to various edge loadings symmetrically on a pair of opposite free edges. We'll discuss the least critical loadings when the buckling of rectangular plates acted on bv a pair of concentrated forces, uniformly distributed loads, locally uniform distributed loads, distributed loads in the form of triangle and a pair of concentrated couples occur respectively.
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[1] Timoshenko,S.,Theory of Elastic Stability(1936). [2] Rayleigh,J.W.S.,Theory oj Sound,Macmillan and Co.Ltd.,London(1877). [3] Ritz, W.,Uber eine neue Methode zur Lösung gewisser Yariationsprobleme der Mathematischen Physik, Jour, für die refine and angewandte Mathematik,135 (1908),1-61 -
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