任意形状弹性薄板弯曲的精确解*
An Exact Method of Bending of Elastic Thin Plates with Arbitrary Shape
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摘要: 本文提供了一个求解任意形状弹性薄板弯曲的新方法,在求得了极坐标系中弹性薄板弯曲微分方程的精确解后,将解代入薄板的边界条件,利用Fourier级数将边界方程展开,可确定出各待定常数,所得结果是精确的。Abstract: This paper presents a new method exactly to solve the bending of elastic thinplates with arbitrary shape. First the analytic solution of differential equation ofelastic thin plate is derived in polar coordinate, then the analytic solution is substituted into the boundary conditions of elastic thin plate with arbitrary shape. The boundaryequations are expanded along the boundary by the use of Fourier series, all unknown coefficients can be decided. The results are exact.
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Key words:
- elastic thin plate /
- flexible bending /
- exact analytic solution
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[1] 张福范,《弹性薄板》,第二版,科学出版社,北京〔1984). [2] 钱伟长,《变分法及有限元》,科学出版社,北京(1980). [3] 张福范,悬臂矩形板的不对称弯曲,固体力学学报5(2)(1980),170-182. [4] 谢秀松、王磊,梯形板弯曲问题的康托洛维奇解,应用数学和力学,5(3)(1984),399-410 [5] S.铁摩辛柯,《板壳理论》,科学出版社,北京(1977). -
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