An relative gain array-based method for calculating the spatial coupling degree of artificial boundary conditions
HOU Hongwei1，LI Jianbo1，LI Zhiyuan2，LI Yanpeng3
(1. State Key Laboratory of Coastal and Offshore Engineering，Dalian University of Technology，Dalian，Liaoning 116024，China；
2. Earthquake Engineering Research Center，China Institute of Water Resources and Hydropower Research，Beijing 100038，
China；3. Anhui Key Laboratory of Architectural Structure and Underground Engineering，
Anhui Jianzhu University，Hefei，Anhui 230009，China)
Abstract：High-precision artificial boundaries are generally characterized by spatio-temporal coupling，but the lack of corresponding quantitative evaluation indexes makes the current assessment of the spatial coupling state of artificial boundaries extremely limited. For this purpose，a computational method for evaluating the spatial coupling state of high-precision artificial boundaries is proposed based on the relative gain array(RGA). The method makes up for the insufficiency of the traditional linear system theory in which the coupling degree only describes the number of fixed degrees of freedom of the system by solving the –norm of the difference matrix of both the RGA and the identity matrix，and choosing the mean-square value about the total elements of the matrix to be defined as the mean coupling degree. The correctness of the proposed method is verified with a viscoelastic artificial boundary，and the reasonableness and applicability of the evaluation results of the method are investigated by using the Thin-Layer Method(TLM) and Scaled Boundary Finite Element(SBFEM) method. The effects of different foundation areas and near-field damping on the spatial coupling characteristics of high-precision artificial boundaries are analyzed，and the feasibility of setting a limit to and rounding off the tiny elements of the dynamic stiffness matrix as a kind of decoupling method for high-precision artificial boundaries is discussed. The results show that the spatial coupling calculation method of artificial boundary conditions proposed in this paper has reasonable applicability，and the decoupling method adopted significantly reduces the storage cost.
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2024, Vol. 43 
