一维C^1有限元超收敛解答计算的EEP法  

COMPUTATION OF SUPER-CONVERGENT SOLUTIONS IN ONE-DIMENSIONAL C^1 FEM BY EEP METHOD

作　　者：袁驷[1] 王枚[1] 和雪峰[1] 

机构地区：[1]清华大学土木工程系,北京100084

出　　处：《工程力学》2006年第2期1-9,共9页Engineering Mechanics

基　　金：国家自然科学基金(50278046);教育部博士点基金联合资助项目(97000315)

摘　　要：将新近提出的C0有限元后处理中超收敛解答计算的单元能量投影(Element Energy Projection,简称EEP)法推广到一维C1类有限元。根据单元投影定理具体推导了一般梁单元的计算公式,并对两个有代表性的单元给出了数值算例。分析和算例表明,EEP法在一维C1类有限元中再次获得令人满意的效果,即对任一单元中的任一点,从位移一直到三阶导数(如梁的挠度、转角、弯矩、剪力),匀可获得与结点位移精度相当的超收敛结果,而且可精确满足自然边界条件。The newly proposed Element Energy Projection （EEP） method has been applied to computing super-convergent solutions in one-dimensional C^1 FEM in this paper. General formulas based on EEP theorem were derived and illustrative numerical examples using two typical elements were given. Both theoretical analysis and numerical examples show that the EEP method also works very well for C^1 problem and successfully gives super-convergent solutions for both displacements （deflections and rotations） and stresses （bending moments and shear forces） at any point on an element, and the accuracy of so-calculated solutions is well comparable to that of nodal displacements. Furthermore, the natural boundary conditions are exactly satisfied automatically by the EEP method.

关 键 词：有限元 一维C^1问题 后处理 超收敛 单元能量投影 

分 类 号：TU318[建筑科学—结构工程]