均布荷载下悬臂矩形板的弯曲
Bending of Uniformly Loaded Cantilever Rectangular Plates
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摘要: 在薄板理论中,悬臂矩形板的弯曲,长期以来是个难题,因而,现有的解均属于近似解,如列出几位曾解过这问题的作者,可提到L.V.Kantorovich,D.L.Holl,W.A.Nash,H.J.Plass,Jr.等.他们所用的方法为变分法或差分法.本文将作出一个精确解.它满足微分方程及复杂的边界条件,包括自由角点条件.在我们的方法中,用了叠加法及广义简支边这概念.它的特点是:沿边各点的弯矩为零,但挠度是存在的,因而要满足自由边的条件.只须消除剩余的剪力.顾及自由角点的位移,只须叠加符合要求的一些简单的弯曲面方程.所得的结果与近似解很好地核对,充分证实了现在这解是正确的.Abstract: In the theory of thin plates,the bending of cantilever rectangular plates has long remained one of the most difficult problems in this field of study. As a consequence the solution now available are all limited to the approximate ones.
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[1] Holl,D.L.,Cantilever Plate with Concentrated Edge Load,Journal of Applied Mechanics,4,(1937). [2] Nowaski.W.,A Contribution to the Theory of Plates and Shells.中国科学院力学研究所. [3] Nach,W.A.,Several Approximate Analysis of the Bending of a Rectangular Cantilever Plate by Uniform Normal Pressure.Journal of Applied Mechanics.19,1(1952). [4] Plass,H.J.,Games Jr.J.H.,Newson C.D.,Application of Reissner’s Variational Principle to Cantilever Plate Deflection and Vibration Problems.Journal of Applied Mechanics,29,(1962). [5] 舒德坚,施振东,弹性薄板广义变分原理及其应用,北京航学院学报,1957.第1期. [6] 张福范.悬臂矩形板的弯曲(有一集中力作用于自由边的中点)清华学报19卷2期1979. [7] 张福范,《弹性薄板》科学出版社,1965. [8] 张福范,悬臂矩形板的弯曲Ⅱ.(弯曲面为不对称的一般情形).未发表. -
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