平面弹性方程的非协调有限元分析  

Nonconforming Finite Elements for the Equation of Planar Elasticity

作　　者：杨永琴[1] 肖留超[2] 陈绍春[1] 

机构地区：[1]郑州大学数学系,郑州450001 [2]河南工业大学理学院,郑州450001

出　　处：《应用数学和力学》2010年第12期1454-1464,共11页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10771198;11071226);河南省国际科技合作项目

摘　　要：针对纯位移平面弹性问题,构造了两个无闭锁非协调有限元,单元对于Lamé常数λ一致收敛,证明了能量模和L2模误差分别为O(h2)和O(h3).最后给出了数值试验验证了理论分析的正确性.Two new locking-free nonconforming finite elements for the pure displacement planar elasticity problem were presented.Convergence rates of the elements were uniformly optimal with respect to λ.The energy norm and L^2 norm errors were proved to be O（h^2） and O（h^3）,respectively.Lastly,numerical tests are carried out,which coincide with the theoretical analysis.

关 键 词：平面弹性 无闭锁 非协调有限元 

分 类 号：O242.21[理学—计算数学]