超协调元  

SUPER CONFORMING ELEMENT

作　　者：傅向荣[1] 王钰 赵阳 陈璞[2] 孙树立[2] FU Xiang-rong;WANG Yu;ZHAO Yang;CHEN Pu;SUN Shu-li(Department of Civil Engineering,China Agricultural University,Beijing 100083,China;Department of mechanics and Engineering Science,PeKing University,Beijing 100871,China)

机构地区：[1]中国农业大学土木工程系,北京100083 [2]北京大学力学与工程科学系,北京100871

出　　处：《工程力学》2024年第S01期7-14,共8页Engineering Mechanics

基　　金：国家自然科学基金项目(11672362)。

摘　　要：该文提出一类超协调的单元理论。不同于在普通协调元中采用的线位移协调插值格式,超协调元的单元插值函数首先引入转角自由度等线位移导数的高阶协调假设,并通过积分推导,进而获得超协调的线位移模型。基于超协调元理论,该文构造了一类新型的三结点三角形平板壳元SCT。数值算例表明:与其他类型单元相比,基于超协调元理论的单元具有计算精度高和计算效率好的优势。该文所提出单元理论构造简单,超协调元理论可以成为构造高性能数值算法的一种新的通用理论。Presents a novel finite element method of super conforming theory.Different from the traditional conforming element which takes the conforming displacement as the trial function,the finite element of super conforming theory firstly assumes that the higher derivative such as rotational-displacement is conforming in element,then,the super conforming displacement can be derived from this assumption by quadrature derivation.Based on the super conforming theory,there is a novel way to formulate the triangular shell element with three drilling degrees of freedom,which is named as SCT.The benchmark example shows that the element of SCT has high accuracy and high efficiency compared with other types of element.The proposed strategy to construct element is simple and effective,and the proposed super conforming theory can be used for developing other high performance numerical methods.

关 键 词：超协调理论 壳单元 转角自由度 有限单元法 高阶分片检验 

分 类 号：O241.82[理学—计算数学]