动力点圆力偶作用于弹性全空间的解及其性质*
The Solution of Dynamic Point-Ring-Couple in an Elastic Space and Its Properties
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摘要: 本文给出动力点圆力偶作用于弹性全空间原点的解,并讨论它的性质.将脉冲荷载沿以原点为心、α半径,在z=0平面上的圆周切向均匀分布,当a→0时经积分运算即得问题的解.当此动力点圆力偶的强度按sinωt变化时,在弹性全空间中以z轴为轴,原点为顶点的锥面在任何时刻均为零应力面.以这些锥面为边界的回转体受按sinωt而变化的扭矩作用的动力扭转问题的解可由本文的解得出.Abstract: The solution of dynamic Point-Ring-Couple at the origin, on z=0 plane, in an elastic space is presented and its properties are discussed. Let shocking loads be uniformly distributed, along the direction of circumference, at a circle, on z=0 plane, with radius a and centered at the origin. Then, the solution of our problem is obtained via integral calculation for a→0. When the intensity of this dynamic Point-Ring-Couple is varied with sincot, the cones in the elastic space with apex at the origin and the z-axis be its symmetric axis, become zero stressed surfaces at any time instance. The solution of dynamic torsion problem of revolution solids with these cones as boundary under the application of torque varied with sinωt is found.
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Key words:
- point-ring-couple /
- torsion problem /
- elastodynamics
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[1] 云天铨,“点圆力偶”作用于弹性全空间的解及其应用,华中工学院学报,2(7) (1962), 86101. [2] 云天铨,回转体扭转问题的一个积分方程解法.华中工学院学报,(3) (1979), 97-104, (MR#81m:73028) [3] 云天铨,嵌入弹性半空间的弹性迥转轴的扭转,应用数学和力学,11(6) (1990), 489-498. [4] Eringen,A.C.and E.S.Suhubi, Elostodynomics,Academic Press, New York(1975). [5] 谢贻权、林钟祥、丁皓江编.咤弹性力学》,浙江大学出版社(1988), 47, -
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