一种基于相对增益矩阵的人工边界条件空间耦合度计算方法

doi:10.13722/j.cnki.jrme.2023.0679

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摘要高精度的人工边界一般具有时空耦合特征，但由于缺乏相应的定量评价指标，使得目前在评估人工边界的空间耦合状态时受到极大的限制。为此，基于相对增益矩阵(RGA)提出一种评价高精度人工边界空间耦合状态的计算方法。该方法通过求解RGA与单位阵两者差值矩阵的 –范数，并选取关于矩阵总元素的均方值定义为均值耦合度，弥补了传统线性系统理论中耦合度仅能描述系统固定自由度数目的不足。以黏弹性人工边界验证所提方法的正确性，并采用薄层法(thin-layer method，TLM)与比例边界有限元法(scaled boundary finite element method，SBFEM)研究该方法评价结果的合理性和适用性。分析不同地基区域范围以及近场阻尼对高精度人工边界空间耦合特征的影响，讨论对动刚度矩阵微小元素进行设限取舍作为高精度人工边界一种解耦方式的可行性。结果表明，提出的人工边界条件空间耦合度计算方法具备良好的适用性，采用的解耦方式显著地降低了存储成本。

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	侯红伟1
	李建波1
	李志远2
	李艳朋3

关键词 ：地基基础工程, 土&ndash, 结构动力相互作用, 高精度人工边界, 时空耦合, 相对增益矩阵, 均值耦合度

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.

Key words： foundation engineering soil-structure dynamic interaction high precision artificial boundary space-time coupling relative gain array(RGA) mean coupling degree

引用本文:

侯红伟1，李建波1，李志远2，李艳朋3. 一种基于相对增益矩阵的人工边界条件空间耦合度计算方法[J]. 岩石力学与工程学报, 2024, 43(S2): 3885-3894.
HOU Hongwei1，LI Jianbo1，LI Zhiyuan2，LI Yanpeng3. An relative gain array-based method for calculating the spatial coupling degree of artificial boundary conditions. , 2024, 43(S2): 3885-3894.

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https://rockmech.whrsm.ac.cn/CN/10.13722/j.cnki.jrme.2023.0679 或 https://rockmech.whrsm.ac.cn/CN/Y2024/V43/IS2/3885

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