摘要
本文采用四边形面积坐标，并应用广义协调法构造出一个具有１２个自由度的四边形板弯曲单元。单元的挠度场以面积坐标多项式表示，对应于直角坐标ｘ，ｙ的完全三次式和部分四次式，因而单元是完备的广义协调的板单元。应用的１２个协调条件为挠度的四个点协调条件和四个边协调条件，以及法向转角的四个边协调条件。由于面积坐标和直角坐标之间为线性变换关系，因此单元刚度矩阵的推导相当简单。数值算例表明：本文单元具有高精度、收敛性。
A quadrilateral plate bending element with 12 degrees of freedom, ACQ, is developed by using the area coordinate method and the generalized conforming approach. The deflection field of the element is expressed with a polynomial of area coordinates which is corresponding to a polynomial of 4th order in Cartesian coordinates (x,y). The twelve generalized compatibility conditions used are 4 point and 4 line compatibility conditions for the deflection w and 4 line compatibility conditions for the normal slope Ψn. Since the transform relation between area coordinates and Cartesian coordinates is linear, the formulation of the element stiffness matrix is rather simple. Numerical examples show that the present element has the advantage of high accuracy, good convergence, insensitivity to geometric distorsion and reliability.
出处
《工程力学》
EI
CSCD
北大核心
1997年第4期1-10,共10页
Engineering Mechanics
基金
国家自然科学基金
高校博士点基金
煤炭系统留学回国人员科技基金
关键词
面积坐标
四边形元
板弯曲元
广义协调元
area coordinate, quadrilateral element, plate bending element, generalized conforming element
