连续梁分析的样条有限点法及程序设计  

Spline finite point method for continuous beam analysis and program design

作　　者：李秀梅[1] 李萍[1] 黄幸[1] 秦荣[1] 

机构地区：[1]广西大学土木建筑工程学院,工程防灾与结构安全教育部重点实验室,广西南宁530004

出　　处：《广西大学学报（自然科学版）》2014年第4期732-739,共8页Journal of Guangxi University（Natural Science Edition）

基　　金：国家自然科学基金资助项目(51069001);广西教育厅项目(201012M5009)

摘　　要：为研究样条有限点法在多跨连续梁结构分析中的应用,依据梁的跨度和刚度变化把连续梁划分为若干梁段子域,子域内采用均匀的样条结点离散,把子域端部的真实位移和样条结点的广义位移参数作为基本未知量,三次B样条基函数作为位移插值函数,根据总势能泛函及变分原理建立子域的刚度方程。按照子域自由度编码装配结构的刚度方程,建立了连续梁分析的样条有限点法计算格式,并设计了相应的程序流程。该方法适用于不同约束情况及荷载条件下的连续梁计算,典型算例的结果表明该方法的有效性。In order to study the application of spline finite point method in analyzing multi-span con-tinuous beams, basing on the changes of span and section stiffness, a continuous beam was divided into several beam subdomains. Each subdomain was uniformly discretized by spline nodes. The cu-bic B-spline function was used as the interpolation function, and the actual displacements of the end nodes and the generalized parameters of the others were treated as the fundamental variables. Ac-cording to the total potential energy variational principle, the subdomain stiffness equations were es-tablished, and the global stiffness equation of the structure was assembled according to the freedom code of the subdomains. The calculated format of spline finite point method to analyze continuous beams was established, and subsequently, the corresponding computing program flow was designed. The method is suitable for the calculation of continuous beams under various constraints and loading conditions. The results calculated by the proposed method were compared with the analytical solu-tions, and the validity and reliability of the spline finite point method were verified.

关 键 词：连续梁 样条有限点法 程序设计 B样条函数 梁段子域 

分 类 号：TU311.4[建筑科学—结构工程]