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Adaptive coupling of FEM and RKPM formulations for contact and impact problems.

机译：FEM和RKPM配方的自适应耦合解决接触和冲击问题。

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摘要

High strain rate contact-impact with accompanied fragmentation is one of the most challenging problems in computational mechanics. Although substantial effort has been made in recent years in the development of meshfree methods, such as the reproducing kernel particle method (RKPM), for alleviating difficulties associated with mesh distortion and regularity requirement in the numerical modeling of the said problems, issues such as spatial-temporal stability and computational efficiency remain unresolved. In this work, an adaptively coupled FEM-RKPM formulation is proposed and stability analysis is performed for modeling of contact and impact problems. Several FEM-RKPM coupling approximation and discretization are introduced, and an averaged consistent coupling formulation has been proposed to achieve desired accuracy with reduced oscillation near the coupling domain.;A unified stabilized conforming nodal integration (SCNI) for the evolving RKPM and FEM domains is proposed. As such, state and field variables transfer in the discretization transformation between FEM and RKPM is not required. The convergence of the FEM with SCNI domain integration is numerically studied. The results show FEM with SCNI exhibits higher accuracy and better convergence rate than FEM with Gauss integration.;The von Neumann stability analysis of the Lagrangian and semi-Lagrangian RKPM discrete equation of motion has been performed. The stable time step estimation for central difference temporal discretization and RKPM as well as FEM-RKPM spatial discretization with various domain integration methods are derived. The results show a favorable stability in SCNI over DNI and one-point Gauss quadrature. The stability analysis for semi-Lagrangian RKPM formulation also shows that the stability condition is inversely proportional to the local velocity gradient. Meeting this stability condition plays an important role in obtaining stable numerical solution in the contact-impact problems.;A new particle based kernel contact algorithm for multi-body contact-impact in proposed. The partition of unity contact detection approach is introduced to identify the potential contact particles. In this approach, the non-penetration condition is naturally achieved by kernel interaction of the contacting bodies. A frictional kernel contact constitutive law suitable for meshfree methods is proposed for modeling the stick-slip condition in frictional contact.;The gradient type stabilization, GSCNI, is proposed to improve the stability condition for RKPM with SCNI domain integration in transient problems. The eigenvalue analysis shows that with the additional gradient stabilization, the non-zero energy oscillatory modes in SCNI are removed.;The proposed methods are applied to model several earth-moving and fragment contact-impact problems. The reliability of the proposed methods is validated by comparison of some simulation results with experimental data showing reasonable agreement.
机译：高应变率接触碰撞并伴有破碎现象是计算力学中最具挑战性的问题之一。尽管近年来在无网格方法（如再生核粒子方法（RKPM））的开发方面做出了巨大的努力，以减轻与网格变形相关的困难和在所述问题的数值建模中的规则性要求，例如空间问题。时间稳定性和计算效率仍未解决。在这项工作中，提出了一种自适应耦合的FEM-RKPM公式，并进行了稳定性分析以对接触和撞击问题进行建模。介绍了几种FEM-RKPM耦合近似和离散化方法，并提出了一种平均一致的耦合公式，以实现所需的精度，同时减小了耦合域附近的振荡。建议。这样，不需要在FEM和RKPM之间的离散化转换中传递状态变量和字段变量。数值研究了有限元法与SCNI域集成的收敛性。结果表明，与高斯积分的有限元法相比，采用SCNI的有限元法具有更高的精度和更好的收敛速度。进行了Lagrangian和半Lagrangian RKPM离散运动方程的von Neumann稳定性分析。推导了采用各种域积分方法的中心差时间离散化和RKPM以及FEM-RKPM空间离散化的稳定时间步长估计。结果表明，SCNI在DNI和单点高斯正交上具有良好的稳定性。半拉格朗日RKPM公式的稳定性分析还表明，稳定性条件与局部速度梯度成反比。满足该稳定性条件对于获得接触冲击问题的稳定数值解具有重要的作用。提出了一种基于粒子的多体接触冲击核接触算法。介绍了统一接触检测方法的分区，以识别潜在的接触粒子。在这种方法中，非渗透条件自然是通过接触体的核相互作用来实现的。提出了一种适用于无网格法的摩擦核接触本构律，对摩擦接触中的粘滑条件进行了建模。提出了梯度型稳定性GSCNI，以改进瞬态问题中具有SCNI域积分的RKPM的稳定性条件。特征值分析表明，通过附加的梯度稳定化，消除了SCNI中的非零能量振荡模式。通过将一些仿真结果与表明合理一致性的实验数据进行比较，验证了所提方法的可靠性。

著录项

  • 作者

    Guan, Pai-Chen.;

  • 作者单位

    University of California, Los Angeles.;

  • 授予单位 University of California, Los Angeles.;
  • 学科 Engineering Civil.;Engineering Mechanical.
  • 学位 Ph.D.
  • 年度 2009
  • 页码 156 p.
  • 总页数 156
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 建筑科学;机械、仪表工业;
  • 关键词

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