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| Hybrid shape functions and Gurtin variational principle based on temporal finite element method for dynamic analysis |
| Received:June 12, 2023 Revised:July 14, 2023 |
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| DOI：10.7511/jslx20230612002 |
| KeyWord:dynamic analysis hybrid shape functions temporal finite element gurtin variational principle weighted residual method |
| Author | Institution |
| 陈凤玲 |
大连理工大学 工程力学系 工业装备结构分析优化与CAE软件全国重点实验室, 大连 |
| 何宜谦 |
大连理工大学 工程力学系 工业装备结构分析优化与CAE软件全国重点实验室, 大连 |
| 于洋 |
大连理工大学 工程力学系 工业装备结构分析优化与CAE软件全国重点实验室, 大连 |
| 杨海天 |
大连理工大学 工程力学系 工业装备结构分析优化与CAE软件全国重点实验室, 大连 |
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| 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. |
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