C-Bézier基函数在稳态线弹性方程求解中的应用  

Application of C-Bézier Basis Function in Solving Steady Linear Elasticity Equations

作　　者：孙兰银 庞琨琨 SUN Lanyin;PANG Kunkun(College of Mathematics and Statistics,Xinyang Normal University,Xinyang 464000,China)

机构地区：[1]信阳师范大学数学与统计学院,河南信阳464000

出　　处：《信阳师范学院学报（自然科学版）》2024年第2期197-202,共6页Journal of Xinyang Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11801490);河南省高校科技创新人才支持计划项目(22HASTIT021);河南省重点研发与推广专项(科技攻关)项目(212102210394)。

摘　　要：用有限元方法求解稳态线弹性方程,以C-Bézier基函数作为参考元上的形函数,通过选取适当的形状参数,在步长不变的情况下,所得到的数值解精度比传统的Lagrange基函数在L∞、L 2范数下高3个数量级以上,在H 1半范数下高2~6个数量级,充分说明了C-Bézier基函数在求解稳态线弹性方程时具有更好的逼近效果。The finite element method was used to deal with the steady linear elasticity equations,and the C-Bézier basis function was used as the shape function on the reference element of the elasticity equations.By selecting the appropriate shape parameters,the accuracy of the numerical solution was three orders of magnitude higher than that of the traditional Lagrange basis in L∞、L 2 norm and 2~6 orders of magnitude higher in H 1 semi-norm.It sufficiently showed that C-Bézier basis has better approximation effect in simulating steady linear elasticity equations.

关 键 词：稳态线弹性方程 有限元方法 C-Bézier基函数 

分 类 号：O242.1[理学—计算数学]