一类平面弹性问题的有限元分析  

The Finite Element Analysis for a Group of Plane Elasticity Problems

作　　者：熊敏[1] 权晓曦 王娟 李昊天 曹一骄 XIONG Min;QUAN Xiaoxi;WANG Juan;LI Haotian;CAO Yijiao(Chengdu Aeronautic Polytechnic,Chengdu 610100,China)

机构地区：[1]成都航空职业技术学院,成都610100

出　　处：《成都航空职业技术学院学报》2023年第1期70-71,75,共3页Journal of Chengdu Aeronautic Polytechnic

摘　　要：针对一类平面弹性振动问题提出了一种新的时空有限元方法。针对此弹性问题,对位移在时间上采用连续元,空间上采用非协调不完全二次矩形有限元进行离散,提出了变分有限元格式。证明了此格式解的存在唯一性,给出了误差估计,并用数值算例验证了理论结果。此方法能改进时空有限元方法在数值实验中计算量大的问题。The new space-time finite element method is proposed for the vibration problems of plane elasticity.In the time directions,a continuous element is used to discretize the displacement.In the space directions,a nonconforming rectangle finite element is used to discretize.A variational finite element scheme is proposed for the elastic problem.The existence and uniqueness of the solutions are proved for the scheme.The deviation estimate is given.Numerical examples are used to verify the theoretical results.This method can improve the problem of large amount of computation in the numerical experiment of the space-time finite element method.

关 键 词：平面弹性问题 时空有限元 存在唯一性 误差估计 

分 类 号：O242[理学—计算数学]