三维一致粘弹性人工边界及等效粘弹性边界单元
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摘要
基于粘弹性人工边界推导了三维一致粘弹性人工边界单元的刚度及阻尼矩阵,利用单元矩阵等效原理采用普通有限单元构造了等效粘弹性边界单元来模拟三维粘弹性边界。均匀半空间算例与成层半空间算例证明三维粘弹性边界单元具有与集中粘弹性人工边界相近的精度,并且施加更为简便。
The stiffness and damping matrixes of 3D consistent artificial boundary are deduced through viscous-spring artificial boundary theory. 3D equivalent viscous-spring artificial boundary element is developed by comparing the matrixes of general finite element and consistent viscous-spring artificial boundary. This boundary element is applied to uniform and layered half space problems, respectively. The results show that 3D equivalent viscous-spring boundary element has the same precision as viscous-spring artificial boundary, and the former is more applicable and simple.
The stiffness and damping matrixes of 3D consistent artificial boundary are deduced through viscous-spring artificial boundary theory. 3D equivalent viscous-spring artificial boundary element is developed by comparing the matrixes of general finite element and consistent viscous-spring artificial boundary. This boundary element is applied to uniform and layered half space problems, respectively. The results show that 3D equivalent viscous-spring boundary element has the same precision as viscous-spring artificial boundary, and the former is more applicable and simple.
引文
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[2]刘晶波,吕彦东.结构-地基动力相互作用问题分析的一种直接方法[J].土木工程学报,1998,31(3):55~64.Liu Jingbo,Lu Yandong.A direct method for analysis of dynamic soil-structure interaction[J].China Civil Engineering Journal,1998,31(3):55~64.(in Chinese)
[3]刘晶波,王振宇,杜修力,杜义欣.波动问题中的三维时域粘弹性人工边界[J].工程力学,2005,22(6):46~51.Liu Jingbo,Wang Zhenyu,Du Xiuli,Du Yixin.Three dimensional viscous-spring artificial boundaries in time domain for wave motion problems[J].Engineering Mechanics,2005,22(6):46~51.(in Chinese)
[4]刘晶波,王振宇,张克峰,裴欲晓.考虑土-结构相互作用大型动力机器基础三维有限元分析[J].工程力学,2002,19(3):34~38.Liu Jingbo,Wang Zhenyu,Zhang Kefeng,Pei Yuxiao.3D finite element analysis of large dynamic machine foundation considering soil-structure interaction[J].Engineering Mechanics,2002,19(3):34~38.(in Chinese)
[5]周爱红,张鸿儒,袁颖,张艳敏.复合地基不同参数对地面动力特性的影响分析[J].中国安全科学学报,2005,15(11):3~6.Zhou Aihong,Zhang Hongru,Yuan Ying,Zhang Yanmin.Effect analysis of composite foundation parameters on ground dynamic characteristics[J].China Safety Science Journal,2005,15(11):3~6.(in Chinese)
[6]潘旦光,楼梦麟,董聪.一致输入作用下土层的地震反应分析[J].计算力学学报,2005,22(5):562~567.Pan Danguang,Lou Menglin,Dong Cong.Seismic response analysis of soil layer under uniform excitation[J].Chinese Journal of Computational Mechanics,2005,22(5):562~567.(in Chinese)
[7]王振宇.大型结构-地基系统动力反应计算理论及其应用研究[D].北京:清华大学,2002.Wang Zhenyu.Computational theory of dynamic response of large structure-soil systems and its application[D].Beijing:Tsinghua University,2002.(in Chinese)
[8]谷音.结构-地基动力相互作用问题高效数值方法研究及工程应用[D].北京:清华大学,2005.Gu Yin.Theoretical analysis of the efficient numerical method for soil-structure dynamic interaction and its application[D].Beijing:Tsinghua University,2005.(in Chinese)
[9]徐芝伦.弹性力学[M].北京:高等教育出版社,1990.Xu Zhilun.Elasticity mechanics[M].Beijing:Higher Education Press,1990.(in Chinese)
[10]刘晶波,谷音,杜义欣.一致粘弹性人工边界及粘弹性边界单元[J].岩土工程学报,2006,28(9):1070~1075.Liu Jingbo,Gu Yin,Du Yixin.Consistent viscous-spring artificial boundary and viscous-spring boundary element[J].Chinese Journal of Geotechnical Engineering,2006,28(9):1070~1075.(in Chinese)
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