平面曲梁面外自由振动有限元分析的p型超收敛算法  

A p-TYPE SUPERCONVERGENT RECOVERY METHOD FOR FINITE ELEMENT ANALYSIS OF OUT-OF-PLANE FREE VIBRATIONS OF PLANAR CURVED BEAMS

作　　者：叶康生[1] 梁童 YE Kang-sheng;LIANG Tong(Department of Civil Engineering,Tsinghua University,Key Laboratory of Civil Engineering Safety and Durability of China Education Ministry,Beijing 100084,China)

机构地区：[1]清华大学土木工程系,土木工程安全与耐久教育部重点实验室,北京100084

出　　处：《工程力学》2020年第10期17-27,共11页Engineering Mechanics

基　　金：国家自然科学基金项目(51078198);清华大学自主科研计划项目(2011THZ03)。

摘　　要：该文用p型超收敛算法对平面曲梁面外自由振动问题进行求解。该法基于频率和振型结点位移在有限元解答中的超收敛特性,在单元上建立振型近似满足的线性常微分方程边值问题,用更高次元对该线性边值问题进行有限元求解获得各单元上振型的超收敛解,将振型的超收敛解代入Rayleigh商,得到频率的超收敛解。该法作为后处理法,修复计算分别在各个单元上单独进行,故通过少量计算即能显著提高频率和振型的精度和收敛阶。数值算例显示该法稳定、高效,值得进一步研究和推广。It extends the p-type superconvergence recovery method to the finite element analysis of the out-ofplane free vibrations of planar curved beams.Based on the superconvergence properties on frequencies and nodal displacements in modes,a linear ordinary differential boundary value problem(BVP)which approximately governs the mode on each element is set up.This linear BVP is solved by using a higher order element from which the mode on each element is recovered.By substituting the recovered mode into the Rayleigh quotient,the frequency is recovered.This method is a post-processing approach.Its recovery computation for each element is handled only on its own domain.It can enhance the accuracy and convergence rate of the frequencies and modes significantly with a small computation cost.Numerical examples demonstrate that the method is stable,efficient and worth further exploring.

关 键 词：平面曲梁 面外自由振动 有限元 p型超收敛 RAYLEIGH商 

分 类 号：TU311.3[建筑科学—结构工程]