一种改进的4节点组合杂交轴对称元

AN IMPROVED FOUR-NODE COMBINED HYBRID AXISYMMETRIC FINITE ELEMENT

在利用能量协调条件构造应力模式时,最后的应力模式中含有矩阵的逆.这个矩阵是否可逆,只有在具体的数值算例中验证.本文将"逆规则"应用于轴对称元应力模式的推导过程中,这样简化了求逆矩阵的形式,从而能够从理论上证明出这个矩阵在常见的几种网格剖分情况下是可逆的.经过这样的简化,最后得到的轴对称元仍具有较好的数值精度和性能,它不发生Poisson闭锁,对单元畸变影响的敏感度小.

When the stress mode is constructed by energy compatibility condition, the last stress mode involves the inverse matrix. Commonly, the reversibility is validated by example problems. In this paper, the ＇inversion crime＇ is used into the deduction of stress mode, so the matrix form is simple and the matrix＇s reversibility is proved in mathematics. By the use of ＇inversion crime＇, the resulting elements exhibit better results in displacements and stresses and excellent performance at nearly incompressible limit and distortions of the element geometry.