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基于五次B样条的子区间法
引用本文:张锡治,闫澍旺,闫玥,崔旭明. 基于五次B样条的子区间法[J]. 天津大学学报(自然科学与工程技术版), 2008, 41(1): 58-64
作者姓名:张锡治  闫澍旺  闫玥  崔旭明
作者单位:[1]天津大学建筑设计研究院,天津300072 [2]天津大学建筑工程学院,天津300072 [3]天津大学机械工程学院,天津300072
摘    要:重构细分划了时域,细分划拓展了0次B样条醒的定义,对高次B样条的递推式进行了拓展,获得了细分划拓展的均匀分划的分段式五次B样条函数,因而拓展了展开定理,构造了五次B样条基函数.该基函数与现有的五次B样奈基函数相比,表征的物理概念更清晰和简洁.基于五次B样条基函数,提出和推导了结构动力响应研究中的位移元子区间法和子区间法的嵌套方法递推格式.通过精度比较,得出子区间法的嵌套方法要优越于位移元子区间法.

关 键 词:五次B样条  结构动力响应  子区间法  位移元  嵌套方法  递推格式
文章编号:0493-2137(2008)01-0058-07
收稿时间:2007-05-14
修稿时间:2007-08-20

Subinterval Method Based on Quintic B-Spline
ZHANG Xi-zhi,YAN Shu-wang,YAN Yue,CUI Xu-ming. Subinterval Method Based on Quintic B-Spline[J]. Journal of Tianjin University(Science and Technology), 2008, 41(1): 58-64
Authors:ZHANG Xi-zhi  YAN Shu-wang  YAN Yue  CUI Xu-ming
Affiliation:ZHANG Xi-zhi, YAN Shu-wang, YAN Yue, CUI Xu-ming (1. Architectural Design and Research Institute of Tianjin University, Tianjin 300072, China; 2. School of Civil Engineering, Tianjin University, Tianjin 300072, China; 3. School of Mechanical Engineering, Tianjin University, Tianjin 300072, China)
Abstract:A time domain was reconstructed and subdivided, the definition of zero order B-spline B^0 was subdivided and extended, and the recurrence relation for the higher order B-spline was extended. Therefore the uniformly-divided piece-wise quintic B-spline function after being subdivided and extended was obtained. Correspondingly, the quintic B-spline basis function was constructed by extending the expansion theorem. In comparison with the existing quintic B-spline basis function, the constructed basis function represents the physical concepts more clearly and concisely. Also, based on the quintic B-spline basis function, the recurrence algorithrns of the subinterval method of displacement element and its nestification method in the research into the structural dynamic response was developed and derived. By comparison of the accuracy, the results showed that the nestification method of subinterval method is better than the subinterval method of displacement element.
Keywords:quintic B-spline   structural dynamic response   subinterval method   displacement element   nestification method   recurrence algorithm
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