几何非线性样条有限元法  

SPLINE FINITE ELEMENT FOR GEOMETRIC NONLINEAR ANALYSIS

作　　者：秦剑[1] 黄克服[2] 张清东[1] 

机构地区：[1]北京科技大学机械工程学院,北京100083 [2]北京大学工学院,北京100871

出　　处：《工程力学》2011年第A01期1-4,共4页Engineering Mechanics

基　　金：国家自然科学基金项目(51075031;50675021)

摘　　要：根据样条有限元方法的基本原理,拓展建立了一种几何非线性样条有限元方法。该方法充分利用了样条函数乘积的性质,将样条函数的积分显式地表达出来,使得传统有限元中需要花费大量时间的刚度矩阵计算可以很简单的得到,具有精度高、输入量小、连续性强等优点。它与普通有限元法使用高斯积分计算的精确结果均在高斯积分点上不同,样条有限元所得到的结果均在单元节点上,在数据的后处理方面更为方便和精确。This paper aims at introducing a new geometric nonlinear spline finite element method（spline FEM） according to the principles of spline functions.The integral among two or three B-spline functions can be expressed in evidence by the integral characteristics of spline functions,thusly the element stiffness matrix can be obtained more easily than using the traditional FEM whose computing process is complicated and time-consuming.And it retains advantages of high-precision,small inputs,and strong continuity.In contrast to traditional FEM which employs the Gauss quadrature to gain results on Gauss points,the variables are gained on nodal points in the new spline FEM.This is convenient and accurate in the pre-and post-processing.

关 键 词：有限元 样条 几何非线性 薄板 后屈曲 

分 类 号：TB115[理学—数学]