带旋转自由度的精化非协调平面四边形等参元

对于C~1类不协调元文1]提出了一种精比直接刚度法。本文进一步将其应用到C~0类问题,建立一种带旋转自由度的不协调平面四边形单元,其协调部分是用人Allman插值法建立的单元函数,不协调部分用了四个内部自由度。该单元能保证通过分片试验,保持了单变量有限元列式简单、性能可靠(无多余零能模式及坐标不变性)等长处,同时,还具备多变量有限元(杂交/拟协调元)高精度的优点。算例表明,本文提出的单元收敛、可靠、高精度且高效率。

Refined Non-Conforming Quadrilateral Plane Isoparametric Element with Drilling Degrees of Freedom

The refined direct stiffness method for non-conforming (C1) element method developed by author in paper 1] is used to derive the quadriiateral plane element with drilling degrees of freedom (C0) which includes Allman's conforming displacement function and non-conforning function with four internal displacements. The behavior of the proposed element in respect of coordinate invariance, spurious zero energy modes, the ability to pass the patch test and rational formulation are obtained. A number of examples is used to show the implementation efficiency, accuracy and reliability.