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直角坐标系下层状黏弹性地基Biot固结解析刚度矩阵解

寇磊 白云

寇磊, 白云. 直角坐标系下层状黏弹性地基Biot固结解析刚度矩阵解[J]. 应用数学和力学, 2016, 37(1): 84-96. doi: 10.3879/j.issn.1000-0887.2016.01.007
引用本文: 寇磊, 白云. 直角坐标系下层状黏弹性地基Biot固结解析刚度矩阵解[J]. 应用数学和力学, 2016, 37(1): 84-96. doi: 10.3879/j.issn.1000-0887.2016.01.007
KOU Lei, BAI Yun. Analytical Stiffness Matrixes for Biot Consolidation of Multilayered Viscoelastic Foundations in the Cartesian Coordinate System[J]. Applied Mathematics and Mechanics, 2016, 37(1): 84-96. doi: 10.3879/j.issn.1000-0887.2016.01.007
Citation: KOU Lei, BAI Yun. Analytical Stiffness Matrixes for Biot Consolidation of Multilayered Viscoelastic Foundations in the Cartesian Coordinate System[J]. Applied Mathematics and Mechanics, 2016, 37(1): 84-96. doi: 10.3879/j.issn.1000-0887.2016.01.007

直角坐标系下层状黏弹性地基Biot固结解析刚度矩阵解

doi: 10.3879/j.issn.1000-0887.2016.01.007
基金项目: 教育部长江学者和创新团队发展计划(IRT1029)
详细信息
    作者简介:

    寇磊(1983—),男,博士(通讯作者. E-mail: klyhe@163.com).

  • 中图分类号: TU433

Analytical Stiffness Matrixes for Biot Consolidation of Multilayered Viscoelastic Foundations in the Cartesian Coordinate System

  • 摘要: 基于直角坐标系下Biot固结的基本控制方程,并考虑软土土骨架的黏弹性特性,通过Fourier-Laplace积分变换、解耦变换、微分方程组理论和矩阵理论,推导了黏弹性地基Biot固结三维空间问题和平面应变问题在积分变换域的解析解,进而得到对应问题的单元刚度矩阵. 然后根据对号入座原则组装得到层状黏弹性地基Biot固结对应问题的总体刚度矩阵.通过求解总体刚度矩阵形成的线性代数方程,得到层状黏弹性地基Biot固结对应问题在积分变换域内的解答.最后应用Fourier-Laplace逆变换得到其物理域内的解.对比求解黏弹性Biot固结问题退化的弹性Biot固结问题与已有解答,验证了刚度矩阵计算方法的正确性,为层状黏弹性地基Biot固结问题提供了理论基础.
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出版历程
  • 收稿日期:  2015-10-14
  • 修回日期:  2015-11-28
  • 刊出日期:  2016-01-16

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