| 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 |
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| 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 |
| 投稿时间：2023-06-12 修订日期：2023-07-14 |
| DOI：10.7511/jslx20230612002 |
| 中文关键词: 动力分析 混合形函数 时域有限元 Gurtin变分原理 加权余量法 |
| 英文关键词:dynamic analysis hybrid shape functions temporal finite element gurtin variational principle weighted residual method |
| 基金项目:自然科学基金(11972109,11572068,12072063);国家重点基础研究发展计划(2015CB057804)资助项目. |
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| 中文摘要: |
| 提出一种基于多项式和三角函数混合的形函数及其构造方法,结合Gurtin变分原理和加权余量法,建立了三种时域有限元方程,从而为描述变量的时变特性提供了更灵活和多样的选择。在基于增维降阶一阶动力方程的时域有限元计算中,提出了一种算法稳定的分析方法,当形函数形式、时间步长及节点数给定,可通过数值计算对算法的稳定性进行判定。通过算例对所提方法的有效性进行了数值验证,考虑了多项式、简谐荷载作用下常/变刚度、质量的动力问题,探讨了不同时间有限元建模方式、形函数、插值点个数、时间步长等因素对计算精度和计算效率的影响,并与解析解、Newmark法、中心差分法等进行了比较,得到了满意的结果。 |
| 英文摘要: |
| 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. |
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