An EEP Adaptive Strategy of the Galerkin FEM for Dynamic Equations of Discrete Systems

XING Qin-yan; YANG Xing; YUAN Si

doi:10.21656/1000-0887.370288

Volume 38 Issue 2

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Article Navigation > Applied Mathematics and Mechanics > 2017 > 38(2): 133-143

XING Qin-yan, YANG Xing, YUAN Si. An EEP Adaptive Strategy of the Galerkin FEM for Dynamic Equations of Discrete Systems[J]. Applied Mathematics and Mechanics, 2017, 38(2): 133-143. doi: 10.21656/1000-0887.370288

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An EEP Adaptive Strategy of the Galerkin FEM for Dynamic Equations of Discrete Systems

doi: 10.21656/1000-0887.370288

Department of Civil Engineering, Tsinghua University; Key Laboratory of Civil Engineering Safety and Durability of China Education Ministry, Beijing 100084, P.R.China

Funds: The National Natural Science Foundation of China(51508305；51378293；51078199)

Received Date: 2016-09-21
Rev Recd Date: 2016-11-17
Publish Date: 2017-02-15

Abstract

Abstract

For the solution of structural dynamic equations, generally the accuracy of results and the efficiency of computation both depend on the selection of the time step lengths, which makes the key difficulty for efficient solution of time-dependent problems. With the element energy projection (EEP) super-convergent solution computed at the post-processing stage of the finite element method (FEM) to replace the unknown true solution and then to estimate the error of the conventional FEM solution, the so-called EEP adaptive method can automatically refine the solution mesh and has achieved success in various boundary-value problems with spatial coordinates as the arguments. Based on the Galerkin FEM solution of the weak form, the EEP self-adaptive strategy was introduced and applied to the dynamic equations of discrete systems. As a result, an adaptive mesh was automatically produced in the time domain, and a dynamic displacement solution satisfying the pre-specified error tolerance at any moment was obtained, which leads to a new adaptive computation approach for time-dependent problems.
- discrete system,
- dynamic equation,
- Galerkin finite element method (Galerkin FEM),
- self-adaptive solution,
- element energy projection (EEP)

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References(23)

References

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