## 留言板

 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.
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.

• 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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