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Improvement research on the stability of explicit integration algorithms with 3D viscoelastic artificial boundary elements

Shutao Li (Department of Civil Engineering, Tsinghua University, Beijing, China) (Institute of Defense Engineering, Beijing, China)
Xin Bao (Department of Civil Engineering, Tsinghua University, Beijing, China)
Jingbo Liu (Department of Civil Engineering, Tsinghua University, Beijing, China)
Fei Wang (Department of Civil Engineering, Tsinghua University, Beijing, China) (College of Defense Engineering, Army Engineering University of PLA, Nanjing, China)
Dong Wang (Department of Civil Engineering, Tsinghua University, Beijing, China)

Engineering Computations

ISSN: 0264-4401

Article publication date: 12 April 2023

Issue publication date: 19 April 2023

86

Abstract

Purpose

When explicit integral analysis is performed on a numerical model with viscoelastic artificial boundary elements, an instability phenomenon is likely to occur in the boundary area, reducing the computational efficiency of the numerical calculation and limiting the use of viscoelastic artificial boundary elements in the explicit dynamic analysis of large-scale engineering sites. The main purpose of this study is to improve the stability condition of viscoelastic artificial boundary elements.

Design/methodology/approach

A stability analysis method based on local subsystems was adopted to analyze and improve the stability conditions of three-dimensional (3D) viscoelastic artificial boundary elements. Typical boundary subsystems that can represent the localized characteristics of the overall model were established, and their analytical stability conditions were derived with an analysis based on the spectral radius of the transfer matrix. Then, after analyzing the influence of each physical parameter on the analytical-stability conditions, a method for improving the stability condition of the explicit algorithm by increasing the mass density of the artificial boundary elements was proposed.

Findings

Numerical wave propagation simulations in uniform and layered half-space models show that, on the premise of ensuring the accuracy of the viscoelastic artificial boundary, the proposed method can effectively improve the numerical stability and the efficiency of the explicit dynamic calculations for the overall system.

Originality/value

The stability improvement method proposed in this study are significant for improving the applicability of viscoelastic artificial boundary elements in explicit dynamic calculations and the calculation efficiency of wave analysis at large-scale engineering sites.

Keywords

Acknowledgements

This study is supported by National Natural Science Foundation of China (no. 52108458), China National Postdoctoral Program of Innovative Talents (no. BX20200192), Shuimu Tsinghua Scholar Program (no. 2020SM005) and National Key Research and Development Program of China (no. 2022YFC3003603). Financial support from these organizations is gratefully acknowledged.

Citation

Li, S., Bao, X., Liu, J., Wang, F. and Wang, D. (2023), "Improvement research on the stability of explicit integration algorithms with 3D viscoelastic artificial boundary elements", Engineering Computations, Vol. 40 No. 2, pp. 494-513. https://doi.org/10.1108/EC-08-2021-0468

Publisher

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Emerald Publishing Limited

Copyright © 2023, Emerald Publishing Limited

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