一种精确积分的四结点板弯曲单元

本文从Ｍｉｎｄｌｉｎ／Ｒｅｉｓｓｎｅｒ理论出发,采用一种新的平行四边形母单元和相应的形函数推导四结点板弯曲单元刚度矩阵的精确积分解。弯曲应变和横向剪切应变分别采用不同的插值公式构成单元刚度矩阵。理论和算例分析表明本文方法克服了“闭锁”现象并能应用于很薄的板,单元刚度矩阵计算速度比采用数值积分计算的同类单元的快四倍。

AN ACCURATELY INTEGRATED 4-NODES PLATE BENDING ELEMENT

Based on the Mindlin-Reissner plate theory, a new 4-nodes plate bending element with ac-cureately integrated stiffness matrix has been derived through a new isoparametric transformation of a quadrilateral parent element together with the associated shape function. The element stiffness matrix is formulated such that both the bending effects and the effects of the transverse shear are included through different interpolation. And it has been demonstrated both theoretically and numerically that the use of this element may not lead to the "locking" phenomenon and is applicable to the analyses of very thin plates. Through the use of this element in the FEM, it will be found that the computing speed of the stiffness matrix of elements is slmost four times faster thin that of the similar element using the two-points Gauss integration.