四边形单元面积坐标插值的新方法  

A NEW METHOD OF QUADRILATERAL ELEMENTS BY AREA COORDINATES INTERPOLATION

作　　者：陈娟[1] 李崇君[1] 陈万吉[2,3] 

机构地区：[1]大连理工大学数学科学学院,辽宁大连116024 [2]大连理工大学工业装备结构分析国家重点实验室,辽宁大连116024 [3]沈阳航空工业学院,飞行器结构分析研究所,辽宁沈阳110136

出　　处：《工程力学》2010年第5期45-52,67,共9页Engineering Mechanics

基　　金：国家自然科学基金项目(60533060;10672032;10726067);辽宁省博士启动基金项目(20061060);大连理工大学理科基金项目(SFDUT07001)

摘　　要：该文利用三角形面积坐标插值和B网方法建立了平面四边形样条单元函数,这类单元函数的特点是满足协调条件,4/8/12节点四边形单元函数分别具有1/2/3次完备阶。其中后两个单元函数的完备阶数高于同类等参元和面积坐标广义协调元,并且应力在单元内部连续。该文通过算例测试了这些单元,数值结果显示它们具有高精度并克服了网格畸变的敏感性。A universal technique for developing new plane quadrilateral spline elements is proposed. In this approach,the triangular area coordinate interpolation and the B-net method are employed to establish the formulations,which satisfy the conforming conditions between two adjacent elements. By using 1-,2-and 3-order bivariate spline interpolation bases,three new 4-,8-and 12-node quadrilateral elements are successfully constructed,respectively. The displacement interpolation functions of the new 8-and 12-node elements possess higher order completeness than the corresponding isoparametric quadrilateral elements and the generalized conforming elements by area coordinates,and the resulting stresses are continuous within an element. Some appropriate examples are employed to evaluate the performance of the proposed elements. The numerical results show that the new spline elements present higher precision and are insensitive to mesh distortions.

关 键 词：有限元 四边形单元 三角形面积坐标 B网方法 单元函数完备阶 

分 类 号：O343.1[理学—固体力学] O241.82[理学—力学]