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应变局部化分析的嵌入强间断多尺度有限元法

卢梦凯 张洪武 郑勇刚

卢梦凯, 张洪武, 郑勇刚. 应变局部化分析的嵌入强间断多尺度有限元法[J]. 力学学报, 2017, 49(3): 649-658. doi: 10.6052/0459-1879-16-397
引用本文: 卢梦凯, 张洪武, 郑勇刚. 应变局部化分析的嵌入强间断多尺度有限元法[J]. 力学学报, 2017, 49(3): 649-658. doi: 10.6052/0459-1879-16-397
Lu Mengkai, Zhang Hongwu, Zheng Yonggang. EMBEDDED STRONG DISCONTINUITY MODEL BASED MULTISCALE FINITE ELEMENT METHOD FOR STRAIN LOCALIZATION ANALYSIS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(3): 649-658. doi: 10.6052/0459-1879-16-397
Citation: Lu Mengkai, Zhang Hongwu, Zheng Yonggang. EMBEDDED STRONG DISCONTINUITY MODEL BASED MULTISCALE FINITE ELEMENT METHOD FOR STRAIN LOCALIZATION ANALYSIS[J]. Chinese Journal of Theoretical and Applied Mechanics, 2017, 49(3): 649-658. doi: 10.6052/0459-1879-16-397

应变局部化分析的嵌入强间断多尺度有限元法

doi: 10.6052/0459-1879-16-397
基金项目: 

国家自然科学基金 11232003

国家自然科学基金 11672062

中央高校基本科研业务费 DUT14YQ217

详细信息
    通讯作者:

    2) 郑勇刚, 教授, 主要研究方向:多尺度与多场耦合计算力学.E-mail:zhengyg@dlut.edu.cn

  • 中图分类号: O242.21;O344.3

EMBEDDED STRONG DISCONTINUITY MODEL BASED MULTISCALE FINITE ELEMENT METHOD FOR STRAIN LOCALIZATION ANALYSIS

  • 摘要: 固体材料的应变局部化行为是导致结构破坏失效的重要因素之一,开展相关数值模拟分析对于结构安全性评估具有重要意义。然而由于材料的非均质和多尺度特性,采用传统数值方法进行求解时通常需要从最小特征尺度离散求解的结构,这将大幅度增加计算规模和成本。针对这一问题,本文提出了一种基于嵌入强间断模型的多尺度有限元方法。该方法从粗细两个尺度离散求解模型,首先在细尺度单元上引入嵌入强间断模型来描述单元间断特性,所附加的跳跃位移自由度则通过凝聚技术进行消除,从而保持细尺度单元刚度阵维度不变。其次,提出了一种增强多节点粗单元技术,其可根据局部化带与粗单元边界相交情况自适应动态地增加粗节点,新构造的增强数值基函数可以捕捉细尺度间断特性,完成物理信息从细单元到粗单元的准确传递以及宏观响应的快速分析;再次,在细尺度解的计算中,将细尺度解分解为降尺度解与单胞局部摄动解,从而消除弹塑性分析时单胞内部的不平衡力。最后,通过两个典型算例分析,并与完全采用细单元的嵌入有限元结果进行对比,验证了所提出算法的正确性与有效性。

     

  • 图  1  强间断模型示意图

    Figure  1.  Illustration of the strong discontinuity model

    图  2  局部化单元内角点集合Se+的选取

    Figure  2.  Selection for the corner nodes set Se+ in a discontinuous element

    图  3  (a)多节点粗单元,(b)~(d)分别为1号、9号和5号粗节点的边界指定位移分布图

    Figure  3.  (a) a multi-node coarse element, the distributions of the prescribed boundary values for (b) coarse node 1, (c) coarse node 9 and (d) coarse node 5

    图  4  土柱压缩算例示意图

    Figure  4.  Illustration of the compression test of soil column

    图  5  不同方法作用反力与加载位移的结果比较

    Figure  5.  Results of the reaction force versus the imposed displacement with different methods

    图  6  不同方法竖直位移的云图

    Figure  6.  Contours of the vertical displacement with different methods

    图  7  基础水平加载算例示意图

    Figure  7.  Illustration of the horizontal loading test of the foundation

    图  8  不同方法作用反力与加载位移的结果比较

    Figure  8.  Results of the reaction force versus the imposed displacement with different methods

    图  9  CE8E获得的局部化带扩展图(A~D对应于图 8中的不同时刻,此图中变形放大了5倍)

    Figure  9.  Illustrations of localization band propagation with the CE8E (A~D correspond to different times in Fig. 8, the deformation is scaled by 5 for clarity)

    图  10  不同方法水平位移的云图

    Figure  10.  Contours of the horizontal displacement with different methods

    表  1  土柱材料参数

    Table  1.   Material parameters for the column

    下载: 导出CSV

    表  2  基础材料参数

    Table  2.   Material parameters for the foundation

    下载: 导出CSV
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出版历程
  • 收稿日期:  2016-12-27
  • 网络出版日期:  2017-03-13
  • 刊出日期:  2017-05-18

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