论文部分内容阅读
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、可靠性和对网格畸变不敏感的优点
In this paper, quadrilateral area coordinates are used, and a quadrilateral plate bending element with 12 degrees of freedom is constructed using the generalized coordination method. The unit’s deflection field is represented by an area coordinate polynomial, corresponding to the complete cubic and partial quadratic forms of the rectangular coordinates x, y, and thus the unit is a complete generalized coordinated plate element. The 12 coordination conditions applied are the four-point coordination condition and the four-side coordination condition of the deflection, and the four-sided coordination condition of the normal rotation angle. Due to the linear transformation between the area coordinates and the rectangular coordinates, the derivation of the element stiffness matrix is quite simple. A numerical example shows that this unit has the advantages of high accuracy, convergence, reliability, and insensitivity to grid distortion.