关于弹性矩形混合有限元的两个注记
Two remarks on rectangular mixed finite elements for elasticity
AI总结：
本文提出一种三维线性弹性问题的协调矩形元，通过适度增加应力自由度（24个）避免了顶点自由度，并利用刚体运动近似位移构造了更低阶的协调元对（应力72自由度，位移6自由度）。
摘要：
三维中最低阶非协调矩形元涉及54个应力自由度和12个位移自由度。通过适度增加自由度（应力为24个），我们获得了三维线性弹性问题的协调矩形元。此外，与协调平面矩形元或单纯形元不同，该单元不涉及任何顶点自由度。其次，我们指出可以通过用刚体运动近似位移来构造更低阶的单元。这产生了一对应力具有72个自由度、位移具有6个自由度的协调元。
英文摘要：
The lowest order nonconforming rectangular element in three dimensions involves 54 degrees of freedom for the stress and 12 degrees of freedom for the displacement. With a modest increase in the number of degrees of freedom (24 for the stress), we obtain a conforming rectangular element for linear elasticity in three dimensions. Moreover, unlike the conforming plane rectangular or simplicial elements, this element does not involve any vertex degrees of freedom. Second, we remark that further low order elements can be constructed by approximating the displacement with rigid body motions. This results in a pair of conforming elements with 72 degrees of freedom for the stress and 6 degrees of freedom for the displacement.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
