样条扇形单元
Spline Sectorial Elements
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摘要: 本文在样条分片插值及样条矩形单元的基础之上进而讨论极坐标中二次及三次样条分片插值及样条(圆环)扇形单元.以用于求解圆(环)域与(圆环)扇形域上的各类问题.圆环扇形单元(r≠0)是样条分片插值在极坐标中简单的推广应用,但扇形单元则不然.本文根据扇形单元在r=0处的特殊性对各位移插值函数作了合理的处理,使得该单元即体现了r=0处的几何特性又可以消除该处应变、应力的奇异性.文中给出了用样条(圆环)扇形单元求解平面问题及薄板弯曲问题的数值算例用以说明该单元的效能.Abstract: In this paper, the quadratic and cubic spline local interpolations on a sectorial elemeat in polar coordinates is discussed and a class of spline sectorial elements for analyses of plane and thin plate problems are presented. A reasonable treatment of the assumed displacement fields for elements with nodes at the origin(r=0) is made so that the elemeats can not only characterize the geometrical properties at the origin but also remove the siagularitp of strains and stresses there.Some numerical examples are given to show the efficiency of the proposed elemeats.
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[1] 石钟慈,样条有限元法,计算数学,1,1(1979).50-72. [2] 何广乾、周润珍.林春哲,样条函数法在解板壳问题中的应用,建筑结构学报.2.2(1981).1-9. [3] 袁驷,用三次B样条进行旋转壳有限元分析.建筑结构学报.3,4(1982).25-30. [4] 袁驷,样条矩形单元,计算结构力学及其应用.1,2(1984),41-48. [5] 华东水利学院.《弹性力学问题的有限单元法》.水利电力出版社(1978). [6] Timoshenko,S.aad S.Woinowsky-Krieger,Theory of Plates and Shells,second edition,McGraw Hill Book Company,Inc,(1959). -
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