IMPROVEMENT OF EXPLICIT ALGORITHMS STABILITY WITH VISCO-ELASTIC ARTIFICIAL BOUNDARY ELEMENTS 1)

doi:10.6052/0459-1879-20-224

Abstract

Abstract:

Viscoelastic artificial boundary elements are commonly applied in the analysis of semi-infinite wave propagation problems, which can accurately absorb the scattered waves generated in the calculation domain. However, the mass density, the stiffness and the damping coefficient of the viscoelastic artificial boundary element are different from those of the internal domain. Therefore, the instability often occurs in the boundary region when the explicit time-domain stepwise integration is performed in the overall model, so, the calculation efficiency of the explicit integral for the overall system is affected. Currently, there is no effective solution to this problem which remains to be settled to conduct efficient large-scale wave propagation simulation. For the two dimensional viscoelastic artificial boundary element, we establish the edge subsystem and corner subsystem which can represent the typical characteristics of the overall system, by the analysis method of transfer matrix spectral radius based on the central difference format commonly used, we derive the analytical solutions of the stability conditions of the edge subsystem and corner subsystem. After that, we analyze the influence of various physical parameters of the two dimensional viscoelastic artificial boundary element on the stability conditions, and obtain the method for improving the stability condition of the explicit algorithm by increasing the mass density of the viscoelastic artificial boundary element. The homogeneous and layered half-space examples show that, set the mass density of the internal element as the upper limit of the mass density of the viscoelastic artificial boundary element, the method proposed in this paper can effectively improve the numerical stability of the explicit time-domain integration when using the viscoelastic artificial boundary elements, without affecting the calculation accuracy, and the calculation efficiency can be significantly improved in the explicit dynamic analysis. The model size (distance from the scattered wave source to the artificial boundary) has a little effect on the stability of the explicit integral which can be ignored.

Key words: explicit time domain integration, viscoelastic artificial boundary element, improvement of numerical stability, transfer matrix, spectral radius

CLC Number:

TU311
P315.9

Li Shutao, Liu Jingbo, Bao Xin. IMPROVEMENT OF EXPLICIT ALGORITHMS STABILITY WITH VISCO-ELASTIC ARTIFICIAL BOUNDARY ELEMENTS ¹⁾[J]. Chinese Journal of Theoretical and Applied Mechanics, 2020, 52(6): 1838-1849.

Figures/Tables 15

Fig. 1 Diagrams of 2D viscoelastic artificial boundary element

Fig. 2 Two kinds of nodal subsystems in 2D model

Fig. 3 Corner subsystem

Fig. 4 Edge subsystem

Fig. 5 The variation of corner subsystem stability coefficient with density ratio

Fig. 6 The variation of edge subsystem stability coefficient with density ratio

Fig. 7 The region of numerical stability in the overall system

Fig. 8 The variation of stability coefficient with $R/L$

Fig. 9 Homogeneous half space model

Fig. 10 Time history of the dynamic load

Table 1 Comparison of critical time steps before and after the improvement of the stability in the homogeneous half space model

Fig. 11 Comparison of displacements in $y$ direction of four nodes in the homogeneous model

Fig. 12 Layered half space model

Table 2 Comparison of critical time steps before and after the improvement of the stability in the layered half space model

Fig. 13 Comparison of displacements in $y$ direction of four nodes in the layered model

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IMPROVEMENT OF EXPLICIT ALGORITHMS STABILITY WITH VISCO-ELASTIC ARTIFICIAL BOUNDARY ELEMENTS ¹⁾

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