全局坐标系下有限元形函数的直接构造方法  

DIRECT CONSTRUCTION METHOD OF FINITE ELEMENT SHAPE FUNCTION IN GLOBAL COORDINATE SYSTEM

作　　者：崔孟雷 李春光 庄心善[1] 

机构地区：[1]湖北工业大学土木工程与建筑学院,武汉430068 [2]中国科学院武汉岩土力学研究所岩土力学与工程国家重点实验室,武汉430071

出　　处：《数值计算与计算机应用》2018年第1期28-36,共9页Journal on Numerical Methods and Computer Applications

摘　　要：在有限元分析中,当计算全局坐标系下某坐标点（x,y）的场变量时,往往先通过求解等参逆变换得到该点的局部坐标（ξ,η）,再通过插值函数求得该点的场变量的大小.然而等参逆变换的求解等价于求解一非线性方程组.本文基于Lagrange插值原理和形函数的特点构造了全局坐标系下的形函数,算例表明本文得到的形函数求解简单,精度与常规逆变换相当.In the finite element analysis, when calculating the field variables of a coordinate point（x,y） in the global coordinates, we often get the local coordinates of the point（ξ,η） by solving the inverse isoparametric transformation firstly,and then receive the size of the field variables of the point through the interpolation function. However, solving the inverse isoparametric transformation is equivalent to solve a set of nonlinear equations. The article constructes the interpolation shape function in the global coordinate systemis based on the Lagrange interpolation principal and the characteristics of the shape function, numerical examples show that solving the shape function of in this paper is easy, and the accuracy is equal to the conventional inverse transformation.

关 键 词：有限元 等参逆变换 LAGRANGE插值 全局坐标系 形函数 

分 类 号：O241.82[理学—计算数学]