Transient elastodynamic analysis with a combination of convolution quadrature method and pseudo-initial condition method
ISSN: 0264-4401
Article publication date: 20 December 2018
Issue publication date: 8 February 2019
Abstract
Purpose
The Convolution Quadrature Method (CQM) has been widely applied to solve transient elastodynamic problems because of its stability and generality. However, the CQM suffers from the problems of huge memory requirement in case of direct implementation in time domain or CPU time in case of its reformulation in Laplace domain. The purpose of this paper is to combine the CQM with the pseudo-initial condition method (PICM) to achieve a good balance between memory requirement and CPU time.
Design/methodology/approach
The combined methods first subdivide the whole analysis into a few sub-analyses, which is dealt with the PICM, namely, the results obtained by previous sub-analysis are used as the initial conditions for the next sub-analysis. In each sub-analysis, the time interval is further discretized into a number of sub-steps and dealt with the CQM. For non-zero initial conditions, the pseudo-force method is used to transform them into equivalent body forces. The boundary face method is employed in the numerical implementation. Three examples are analyzed. Results are compared with analytical solutions or FEM results and the results of reformulated CQM.
Findings
Results demonstrate that the computation time and the storage requirement can be reduced significantly as compared to the CQM, by using the combined approach.
Originality/value
The combined methods can be successfully applied to the problems of long-time dynamic response, which requires a large amount of computer memory when CQM is applied, while preserving the CQM stability. If the number of time steps is high, then the accuracy of the proposed approach can be deteriorated because of the pseudo-force method.
Keywords
Acknowledgements
The authors would like to thank the anonymous reviewers and editors for their valuable comments and hard work on this study. This work was supported by the National Science Foundation of China (Number 11702087, 11472102 and 11772125), the Key Research Project of High School of Henan Province (Number 16A520015) and the PhD research startup foundation of Henan Normal University (Number qd15131).
Citation
Li, Y., Zhang, J., Zhong, Y., Shu, X. and Dong, Y. (2019), "Transient elastodynamic analysis with a combination of convolution quadrature method and pseudo-initial condition method", Engineering Computations, Vol. 36 No. 1, pp. 334-355. https://doi.org/10.1108/EC-06-2018-0263
Publisher
:Emerald Publishing Limited
Copyright © 2018, Emerald Publishing Limited