采用解析试函数法构造的抗畸变五节点平面单元

文章以解析试函数法作为工具,以弱式分片试验作为单元收敛判别标准,构造了两个五节点平面单元ATFM5-I和ATFM5-II.这两个单元在边界协调性上分别满足点协调和点-边组合协调条件,位移场均实现了直角坐标的二次完备,因此,消除了采用直角坐标易使单元出现方向性的问题,且当单元形状扭曲时,位移场的完备次数不会随着衰减,从而从根本上保证了单元的抗畸变性能.算例表明,这两个单元都有着良好的精度和收敛性,除了可以作为过渡单元外,还可以用于曲边界问题的拟合.

Two Robust 5-Node Membrane Elements Based on Analytical Trial Functions

Based on the analytical trial functions,two 5-node membrane elements named ATFM5-I and ATFM5-II were proposed.In the formulating,the weak form of patch test was used instead of the strict form;thus,the loose form of conforming conditions can be taken as point and composite form of point-side respectively.The displacement fields of these two elements are all polynomials of second order completion of Cartesian coordinates.Therefore,the problem of orientation was overcome naturally.Furthermore,the complete order of the displacement field would keep invariable when the element was distorted and then the elements became more insensitive to mesh distortion.The numerical results show that the proposed elements are accurate and convergent.