一个简明有效的四边形杂交/混合薄板弯曲单元

A SIMPLE AND EFFECTIVE QUADRILATERAL HYBRID/MIXED THIN PLATE BENDING ELEMENT

本文应用加权残量法基本原理，给出了建立杂交／混合元模型的简明列式，构造了四 边形杂交／混合（多变量）薄板弯曲单元ＱＰ１２元。该单元列式简明，采用自然坐标插值，保持了 坐标的几何不变性：形成单元刚度阵的各矩阵均推出了显式，不需作数值积分，从而避免了 高阶矩阵的求逆运算，提高了计算效率和精度。数值结果表明， ＱＰ１２元的应力、位移精度均 较高，对各种载荷工况和边界支承条件适应性强。

In this paper, a simple formulation of hybrid/mixed finite element is established based on the principle of weighted residual approach. A quadrilateral hybrid/mixed thin plate bending element-QP12 element is constructed. Its geometrical invariability is kept by using natural coordinate interpolation functions. The matrices used in constructing its stiffness matrix are given in explicit forms without involving numerical integration Thus the inverse calculation of high order matrix is avoided and the computational efficiency and precision are increased.The numerical results show that QP12 element has higher accuracy in both stresses and displacements, and has strong adaptability in various load cases and boundary conditions.