用双向三角级数法解悬臂矩形薄板在均布荷载下的弯曲
Solution of Bending of Cantilever Rectangular Plates under Uniform Surface-Load by the Method of Two-Direction Trigonometric Series
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摘要: 悬臂矩形板的弯曲问题是平板理论中的一个难题.多年来,对于这种板只有能量法与数值解法的近似解.1979年以来清华大学张福范教授等用迭加法陆续得出悬臂矩形板在均布荷载和一些集中荷载作用下的解析解.对于在均布荷载作用下的悬臂矩形薄板,本文用双向三角级数法获得了其挠度函数的解析解,并将所得结果与迭加法所得的结果进行了比较.通过比较表明,两种方法计算的结果符合得十分好,因而相互印证了它们的正确性.Abstract: The bending of a cantilever rectangular plate is a very complicated problem in the theory of plates. For a long time, there have been only approximate solutions for this problem by energy methods and numerical methods.since 1979. Prof. F. V. Chang of Tsing Hua University obtained, by the method of superposition, a series of analytic solutions for cantilever rectangular plates under uniform load and concentrated load.In this paper, the two-direction trigonometric series is used to obtain the solution for the bending of cantilever rectangular plates under uniform load. The obtained results are compared with the results by the method of superposition. The comparison shows that the results of these two methods are in good agreement, hence they are mutually confirmed to be correct.
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[1] 张福范,悬臂矩形饭的弯曲(有一集中力作用于自由边的中点),清华大学学报,19,2(1979). [2] 张福范,均布荷载下悬臂矩形板的弯曲,应用数学和力学,1.3(1980),349-362. [3] 张福范,庄不连续荷载作用下的悬臂矩形板的弯曲,应用数学和力学,2,4(1981),369-378. [4] 张福范,悬臂矩形板的不对称弯曲,固体力学学报,2(1980),170-182. [5] 林鹏程,在集中荷载作用下悬臂矩形板的弯曲,应用数学和力学,3,2(1982),249-259. -
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