计算力学学报2024，Vol.41Issue(6)：1012-1019,8.DOI:10.7511/jslx20230612002
基于混合形函数和Gurtin变分原理的动力时域有限元方法
Hybrid shape functions and Gurtin variational principle based on temporal finite element method for dynamic analysis
摘要
Abstract
A kind of hybrid shape functions ars presented using polynomial and trigonometric base functions,and three temporal finite element models are developed utilizing Gurtin variational principle and weighted residual technique,such that variables can be characterized more flexibly to cope with more complex time varying loads.An error transfer formula is derived for the first-order temporal FE model,by which stability analysis can numerically be conducted when the shape functions,time step size,and the numbers of temporal nodes are determined.Various numerical examples with constant/variable stiffness and mass,and polynomial and harmonic excitations are provided to illustrate the efficiency of the proposed approaches,and impacts of different temporal FE models/shape functions,different numbers of interpolation points,and different step sizes,etc.are taken into account.Satisfactory results are achieved in comparison with analytical solutions,results from Newmark method,and Central difference method,etc.关键词
动力分析/混合形函数/时域有限元/Gurtin变分原理/加权余量法Key words
dynamic analysis/hybrid shape functions/temporal finite element/gurtin variational principle/weighted residual method分类
数理科学引用本文复制引用
陈凤玲,何宜谦,于洋,杨海天..基于混合形函数和Gurtin变分原理的动力时域有限元方法[J].计算力学学报,2024,41(6):1012-1019,8.基金项目
国家自然科学基金(11972109,11572068,12072063) （11972109,11572068,12072063）
国家重点基础研究发展计划(2015CB057804)资助项目. （2015CB057804）
