任意变厚度旋转扁薄壳非线性稳定的样条函数解法  

Spline Solution of Nonlinear Stability of Revolving Shallow Shells with Arbitrarily Variable Thickness

作　　者：侯朝胜[1] 李磊 

机构地区：[1]天津大学建筑工程学院,天津300072 [2]中国建筑东北设计院福州分院,福州350011

出　　处：《天津大学学报》2006年第12期1446-1450,共5页Journal of Tianjin University(Science and Technology)

摘　　要：为解决计算矢高特大的扁壳的收敛问题,以三次B样条函数为试函数,用配点法计算了任意变厚度的旋转扁薄壳的非线性稳定.给出了均布或多项式分布荷载作用下,等厚度、线性、指数型或多项式型变厚度的圆锥壳、球壳或四次多项式型旋转壳的上、下临界荷载.所得的结果同其他方法包括有限单元法的结果做了比较.在均布荷载作用下,等厚度球壳的矢高为其厚度的6 052倍时,对上临界荷载的计算仍取得了收敛的数值结果.用样条配点法编写的程序具有精度高、收敛范围特大、输入的数据和计算时间少的优点.With cubic B-spline function taken as trial function, the solution of nonlinear stability of a revolving shallow shell with arbitrarily variable thickness was obtained by the method of point collocation in order to solve the convergence of a shallow shell with big rise. Under action of uniformly or polynomial distributed load, upper and lower critical loads of revolving shells （ including conical shells, spherical shells and quartic polynomial shells） with uniform thickness, linearly, exponentially or polynomial variable thickness were evaluated. All solutions were compared with those obtained by other methods such as the finite elements method. As the rise of a spherical shell with uniform thickness is 6 052 times of its thickness, upper critical load of the shell subjected to uniformly distributed load was investigated, and the convergent result was still derived. Advantages of the program written by the spline collocation method are higher accuracy, wider convergent region, less input data and computing time.

关 键 词：变厚度 旋转壳 非线性稳定 样条配点法 

分 类 号：TU33[建筑科学—结构工程]