轴对称荷载作用下环形薄板大挠度样条函数解法  

Cubic Spline Solution of Large Deflection of Ring Plate Subjected to Axisymmetrical Load

作　　者：侯朝胜[1] 吴双文[1] 

机构地区：[1]天津大学建筑工程学院,天津300072

出　　处：《天津大学学报（自然科学与工程技术版）》2004年第1期50-53,共4页Journal of Tianjin University：Science and Technology

摘　　要：环形薄板的大挠度计算因为边界条件复杂,仅有少数特殊情形的数值解答.这些解均是利用摄动法以某点挠度为摄动参数得到的结果.当这点挠度较大或为零,将出现难以解决的困难.作者以三次B样条函数为试函数,用配点法计算环形薄板的大挠度.荷载可为均布荷载、边缘均布线荷载、边缘均布力矩及它们的组合.在所有的算例中均取得了收敛的数值结果.在均布荷载、边缘均布线荷载、边缘均布力矩作用下的计算结果同摄动法的计算结果作了比较,结果表明,样条函数的方法收敛范围大、精度高和计算时间少.There were only few special numerical solutions to the problem of the large deflection of a ring plate because of the complication of the boundary conditions.These solutions were given by perturbation method,in which a perturbation parameter was the deflection on some location.It would be difficult to solve the problem of the large deflection of the ring plate when the deflection on the location was larger or zero.With cubic B-splines taken as trial function,the large deflection of a thin ring plate was calculated by the method of point collection.Loads might be such types as uniformly distributed load,uniformly distributed line load and uniformly distributed moments along the edges or their combinations.Convergent results were obtained from all the examples.Under the action of the uniformly distributed load,the uniformly distributed line load or the uniformly distributed moment along the edge,the results were compared with that obtained by the perturbation method,which showed that the method of cubic splines had the advantages of wide convergent range,high precision and little computing time.

关 键 词：轴对称 荷载作用 环形薄板 大挠度 样条函数 配点法 

分 类 号：TU33[建筑科学—结构工程]