四边形8-结点Mindlin板单元  

A quadrilateral 8-node Mindlin plate element

作　　者：沈冯强[1] 

机构地区：[1]合肥工业大学土木建筑工程学院,安徽合肥230009

出　　处：《合肥工业大学学报（自然科学版）》2000年第1期144-148,共5页Journal of Hefei University of Technology：Natural Science

基　　金：国家教委留学回国人员科研启动基金

摘　　要：文章提出一个四边形的 8-结点 Mindlin板单元。板的横向位移 w用 8-结点二次型函数插值 ,板的弯曲转角θx和θy用 4 -结点双线性函数插值。在计算与剪应变对应的刚度系数时 ,将横向位移一阶偏导数 w,x与 w,y通过它们在角结点处的值用双线性函数再次插值。以此根除原始 Mindlin板单元固有的自锁现象。本单元的理论合理 ,算法简便 ,易于实现计算机编程 ,计算效率高 ,分析结果准确。它是一个很好的从薄板到厚板范围内的实用有限板单元。A quadrilateral 8 node Mindlin plate element is proposed for unified analysis of plates of all thicknesses. The shape functions used for lateral deflection w are the ones of quadratic serendipity element. The mid plane normal rotations θ x and θ y are interpolated bilinearly through their values at corner nodes. In other words, θ x and θ y are interpolated with shape functions one degree lower than those used for w. In the computation of stiffness coefficients related with lateral shear strains, the first order partial derivatives of w i.e. w ,x and w ,y  are re interpolated through their virgin values at corner nodes with the shape functions used for θ x and θ y . The re interpolation of w ,x and w ,y  is to cure the locking defect inherent with native Mindlin plate elements. The theory underneath the new Mindlin plate element is logical, its algorithm is simple and easy to implement, its numerical solutions are accurate, and the computation is very efficient. Therefore, the new element is a practical unified element for thin and thick plates.

关 键 词：Mindlin板单元 函数 刚度系数 位移 横向剪应变 Kinchhoff薄板理论 

分 类 号：TU339[建筑科学—结构工程]