A stable implicit nodal integration-based particle finite element method (N-PFEM) for modelling saturated soil dynamics
A stable implicit nodal integration-based particle finite element method (N-PFEM) for modelling saturated soil dynamics
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DOI：
10.1016/j.jrmge.2023.11.016
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发表时间：
2024-06-18
影响因子：
7.3
通讯作者：
Lei，Qinghua
中科院分区：
文献类型：
--
作者：
Wang，Liang;Zhang，Xue;Lei，Qinghua
在这项研究中，我们提出了一种新的节点积分为基础的颗粒有限元法（N-PFEM）设计的饱和土壤的动力分析。我们的方法将节点集成技术到广义Hellinger-Reissner（HR）变分原理，创建一个隐式PFEM制定。为了减轻体积锁定问题，在低阶元素，我们采用了基于节点的应变平滑技术。通过在平滑单元的中心离散场变量，我们实现了单元上的节点积分，消除了在PFEM中重新网格化后对复杂映射操作的需要。我们表示离散化的控制方程作为一个最小最大优化问题，这是进一步重新制定为一个标准的二阶锥规划（SOCP）问题。应力，孔隙水压力和位移同时确定使用先进的原对偶内点法。因此，与基于位移的PFEM公式相比，我们的数值模型提高了应力和孔隙水压力的准确性。数值实验表明，N-PFEM有效地捕捉瞬态和长期的高精度饱和土壤的水力力学行为，避免了需要稳定或正则化技术通常采用其他节点集成为基础的PFEM方法。这项工作具有重要意义的发展强大的和准确的数值工具，研究饱和土壤动力学。
In this study, we present a novel nodal integration-based particle finite element method (N-PFEM) designed for the dynamic analysis of saturated soils. Our approach incorporates the nodal integration technique into a generalised Hellinger-Reissner (HR) variational principle, creating an implicit PFEM formulation. To mitigate the volumetric locking issue in low-order elements, we employ a node-based strain smoothing technique. By discretising field variables at the centre of smoothing cells, we achieve nodal integration over cells, eliminating the need for sophisticated mapping operations after re-meshing in the PFEM. We express the discretised governing equations as a min-max optimisation problem, which is further reformulated as a standard second-order cone programming (SOCP) problem. Stresses, pore water pressure, and displacements are simultaneously determined using the advanced primal-dual interior point method. Consequently, our numerical model offers improved accuracy for stresses and pore water pressure compared to the displacement-based PFEM formulation. Numerical experiments demonstrate that the N-PFEM efficiently captures both transient and long-term hydro-mechanical behaviour of saturated soils with high accuracy, obviating the need for stabilisation or regularisation techniques commonly employed in other nodal integration-based PFEM approaches. This work holds significant implications for the development of robust and accurate numerical tools for studying saturated soil dynamics.