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浙江大学学报(工学版)
浙江大学学报(工学版)  2017, Vol. 51 Issue (10): 1996-2004    DOI: 10.3785/j.issn.1008-973X.2017.10.014
土木工程、交通工程     
多边形比例边界有限单元非线性化方法及应用
陈楷1,2, 邹德高1,2, 孔宪京1,2, 刘京茂1,2
1. 大连理工大学 水利工程学院, 辽宁 大连 116024;
2. 大连理工大学 海岸和近海工程国家重点实验室, 辽宁 大连 116024
Novel nonlinear polygon scaled boundary finite element method and its application
CHEN Kai1,2, ZOU De-gao1,2, KONG Xian-jing1,2, LIU Jing-mao1,2
1. School of Hydraulic Engineering, Dalian University of Technology, Dalian 116024, China;
2. State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology, Dalian 116024, China
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摘要：

针对当前比例边界有限元法（SBFEM）仅适用于弹性求解，无法推广至非线性应用的问题；根据三角形单元积分法则，提出在每个线单元径向覆盖的三角形引入域内高斯积分点，通过半解析的弹性解来构造用于非线性分析的单元形函数，实现了非线性多边形比例边界有限单元（NPSBFE）.采用NPSBFE对经典算例Koyna大坝进行塑性损伤动力响应分析，与振动台实验及XFEM模拟结果进行比较，结果基本一致，验证了实现的NPSBFE用于非线性动力分析的可靠性.采用NPSBFE模拟考虑挤压边墙的面板堆石坝弹塑性地震动响应.用较少的网格模拟结果与有限元较密网格所得的结果吻合良好.多边形比例边界有限元可以非常灵活地处理复杂的材料分区及跨尺度区域的网格衔接问题，能够大幅减少建模难度和单元数量，提高模拟效率.
Abstract:

The scaled boundary finite element method (SBFEM) is extensively applied in elastic structure numerical simulation. However, its application cannot be expanded to nonlinear problem. A novel nonlinear polygon scaled boundary finite element (NPSBFE) was developed by introducing internal Gaussian integration points over a subdomain covered by each line element according to the integral rule of triangular element. The nonlinear shape function was constructed with the introduced points by the semi-analytical solution derived from elastic theory. The Koyna concrete dam was modeled, which was always treated as the classical research object for dynamic damage research of concrete dams. The results accorded well with the one obtained from XFEM simulation and shake table test, which verified the reliability of the accomplished method in nonlinear dynamic analysis. The response of nonlinearity under earthquake for a homogeneous concrete faced rockfill dam with extrusion sidewall was modeled by utilizing the NPSBFE and FEM, respectively. Results accorded well with the conclusion obtained from a dense FEM mesh, which indicated the robustness of NPSBFE for dealing with the material partition in complex geometries. The difficulty in modeling and numbers of elements can be significantly reduced. The NPSBFE provided prominent advantages in dealing with the optimization of material partition and cross-scale subdivision in the domain with a mesh size changing rapidly.
收稿日期: 2016-08-29 出版日期: 2017-09-27
CLC:  TV641  
基金资助:

国家重点研发计划资助项目（2017YFC0404900）；国家自然科学基金资助项目（51678113；51379028）；中央高校基本科研业务费资助项目（DUT17ZD219）.
通讯作者: 邹德高,男,教授.ORCID:0000-0002-0551-6538.     E-mail: zoudegao@dlut.edu.cn
作者简介: 陈楷(1991-),男,博士生,从事非线性比例边界有限元数值模拟研究.ORCID:0000-0002-9851-9091.E-mail:chenkai@mail.dlut.edu.cn
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引用本文:

陈楷, 邹德高, 孔宪京, 刘京茂. 多边形比例边界有限单元非线性化方法及应用[J]. 浙江大学学报(工学版), 2017, 51(10): 1996-2004.

CHEN Kai, ZOU De-gao, KONG Xian-jing, LIU Jing-mao. Novel nonlinear polygon scaled boundary finite element method and its application. JOURNAL OF ZHEJIANG UNIVERSITY (ENGINEERING SCIENCE), 2017, 51(10): 1996-2004.

链接本文:

http://www.zjujournals.com/eng/CN/10.3785/j.issn.1008-973X.2017.10.014    或    http://www.zjujournals.com/eng/CN/Y2017/V51/I10/1996

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