基于面积坐标与B网方法的四边形样条单元  

AREA COORDINATES AND B-NET METHOD FOR QUADRILATERAL SPLINE ELEMENTS

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,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,大连116024 [3]沈阳航空工业学院飞行器结构分析研究所,沈阳110136

出　　处：《力学学报》2010年第1期83-92,共10页Chinese Journal of Theoretical and Applied Mechanics

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

摘　　要：传统等参元方法中,S型等参元完备阶较低,对网格畸变敏感,L型等参元具有高阶完备性但需要使用内部节点.另外,由于引入等参变换,采用数值积分可能导致总刚度矩阵出现奇异性.利用三角形面积坐标与B网方法建立了一类平面四边形的样条单元函数,它们的特点是满足协调条件,克服网格畸变敏感性.其中8节点和12节点单元分别为2次和3次样条函数,对直角坐标分别具有二阶和三阶完备性,高于相同节点的S型等参元.通过算例测试了这些样条单元,并与等参元和其它四边形单元比较,数值结果显示了它们的高精度和有效性.In general,there are two types of quadrilateral isoparametric elements,Serendipity type and La-grangian type.The S-type elements only possess low order completeness,and are sensitive to mesh distortions. The L-type elements possess high order completeness,but include interior nodes.By using numerical integrations due to isoparametric transformation,the overall stiffness matrix may remain singular.In this paper, a kind of quadrilateral spline elements are constructed by using triangular area coordinates interpolation and B-net method.These spline elements have property of conformality,and are insensitive to mesh distortions. The 8 and 12-node quadrilateral elements are represented by bivariate splines of degree 2 and 3,respectively. The two elements possess 2 and 3 order completeness in Cartesian coordinates,higher than the corresponding isoparametric elements with the same nodes.Some numerical examples are employed to evaluate the performance of the proposed elements.The results show that the new spline elements present higher precision and efficiency in comparison with other quadrilateral elements.

关 键 词：单元样条函数 8/12节点四边形单元 面积坐标 B网方法 单元完备阶 

分 类 号：O343.1[理学—固体力学]