任意四边形平面问题的样条有限元法  

B-SPLINE FINITE ELEMENT METHOD FOR THE PLANE PROBLEM OF ARBITRARY QUADRILATERAL REGION

作　　者：秦剑[1] 黄克服[1] 

机构地区：[1]北京大学工学院力学与空天技术系,北京100871

出　　处：《工程力学》2010年第6期29-34,共6页Engineering Mechanics

摘　　要：用三次B样条有限元通过坐标变换和变分法求解任意四边形区域上的平面问题,利用分区势能原理推广到由四边形组成的任意平面区域,推导出了具体的计算公式,为平面问题求解提供了一种高效的计算方法。与普通有限单元相比,该方法计算量小,而且计算结果具有对网格畸变不敏感,精度高等显著特点。A spline finite element method（spline FEM） based on double cubic B-spline is presented for obtaining an approximate solution for the plane problem of arbitrary quadrilateral region,where the variational method and coordinate transformation are used.The explicit expression is derived.The proposed method is applied on examples to illustrate the efficiency of spline FEM.It is demonstrated that the spline FEM has better convergence,higher accuracy and is more efficient in computing storage.Moreover,the result is less sensitive to mesh distortion.

关 键 词：样条元 平面问题 坐标变换 任意四边形 几何不敏感 

分 类 号：O241.82[理学—计算数学]