DDA方法中的人工边界问题研究

doi:10.13722/j.cnki.jrme.2014.0176

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摘要数值分析中的人工边界可能会引入虚假的反射波，不可避免地影响求解，针对非连续变形分析(DDA)方法中的人工边界问题，首先，基于Newmark法推导黏性边界、黏弹性边界对DDA方程组的贡献；其次，为更好地解决地震等外源入射问题，在DDA中引入了自由场边界；最后，为保证静、动力分析过程转换时边界的一致性，在DDA中实现静动力统一边界。利用改进后的DDA程序进行算例分析，结果表明：各人工边界理论在DDA程序实施正确；黏性边界能高效地吸收人工边界处的反射波，黏弹性边界可以反映介质的弹性恢复能力；与黏性边界相比，两侧施加自由场边界模拟无限域运动可以减少边界的影响；引入统一人工边界的DDA可以完整地模拟静、动力计算全过程。

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关键词 ：数值分析, 非连续变形分析, 人工边界, 黏性边界, 黏弹性边界, 自由场边界, 静动力统一边界

Abstract：The artificial boundaries in numerical analysis may introduce fictitious scattered waves，which inevitably affect the simulation results. The artificial boundary problem in the discontinuous deformation analysis (DDA) method had been investigated in detail. Firstly，the contributions to the DDA equations for nonreflecting boundaries(including the viscous boundary and the viscoelastic boundary) were deduced based on the Newmark method. Secondly，to accurately simulate the motion due to external source wave such as earthquakes，a free-field boundary in DDA was introduced. Lastly，the unified static-dynamic boundary was implemented in DDA to ensure the consistency of the transformation of the boundaries. The analysis of examples with the improved DDA program showed that each artificial boundary theory has been correctly implemented. The viscous boundary was found to be highly effective for the absorption of the reflection wave at the artificial boundaries，and the viscoelastic boundary adequately simulated the elastic recovery of the infinite domain. The DDA model with the free-field boundaries at both sides is better than that imposed by the viscous boundary. The DDA with the unified boundary can completely simulate the static and dynamic calculation process.

Key words： numerical analysis discontinuous deformation analysis(DDA) artificial boundaries viscous boundary viscoelastic boundary free-field boundary static-dynamic unified boundary

引用本文:

付晓东，盛谦，张勇慧. DDA方法中的人工边界问题研究[J]. 岩石力学与工程学报, 2015, 34(05): 986-993.
FU Xiaodong，SHENG Qian，ZHANG Yonghui. INVESTIGATION ON ARTIFICIAL BOUNDARY PROBLEM IN DISCONTINUOUS DEFORMATION ANALYSIS METHOD. , 2015, 34(05): 986-993.

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http://www.rockmech.org/CN/10.13722/j.cnki.jrme.2014.0176 或 http://www.rockmech.org/CN/Y2015/V34/I05/986

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