Meshfree

RKPM2D Large-strain Computational Framework

by Ahmed Elgamal, Jiun-Shyan Chen, Zhijian Qiu, Jonghyuk Baek, Tsunghui Huang, Haoyan Wei, Jinchi Lu

An effort is proposed to bring the capabilities and advantages of the meshfree method within a dedicated open-source framework for use in earthquake engineering applications.

The open-source RKPM-based meshfree (Chen et al., 2013, 2017a, b; Chen and Belytschko, 2015) computational framework (Huang et al., 2019) for linear static analysis was developed by JS Chen and co-workers. The RKPM2D is available at: https://link.springer.com/article/10.1007/s40571-019-00272-x

Currently, the RKPM2D is being extended to conduct nonlinear large-strain dynamic analysis. As such, a representative simulation of earth embankment subjected to earthquake loading is presented to demonstrate the computational capabilities of this extended RKPM open-source code.

Earthdam Problem



Earthdam


Download RKPM2D Large-strain computational framework for this example:
RKPM2D Large Strain Computational Framework (ver.1, updated 6/26/2021)

References:
1. Chen, J. S., Hillman, M., and Rüter, M. (2013) An Arbitrary Order Variationally Consistent Inte-gration Method for Galerkin Meshfree Methods. International Journal for Numerical Methods in Engineering, 95, 387-418.
2. Chen, J.S., and Belytschko, T. (2015). Meshless and meshfree methods. Encyclopedia of applied and computational mathematics, 886-894.
3. Chen, J.S., Liu, W.K., Hillman, M.C., Chi, S.W., Lian, Y., and Bessa, M.A. (2017a). Reproduc-ing Kernel Particle Method for Solving Partial Differential Equations. Encyclopedia of Computa-tional Mechanics Second Edition, 1-44.
4. Chen, J.S., Hillman, M., and Chi, S.W. (2017b). Meshfree methods: progress made after 20 years. Journal of Engineering Mechanics, 143(4), 04017001.
5. Hillman, M., and Chen, J. S. (2016). An Accelerated, Convergent and Stable Nodal Integration in Galerkin Meshfree Methods for Linear and Nonlinear Mechanics. International Journal for Nu-merical Methods in Engineering, 107, 603-630.
6. Huang, T.H., Wei, H., Chen, J.S., and Hillman, M.C. (2019). RKPM2D: an open-source imple-mentation of nodally integrated reproducing kernel particle method for solving partial differential equations. Computational Particle Mechanics, 1-41.
7. Qiu, Z. and Elgamal, A., 2020. Three-Dimensional Modeling of Strain-Softening Soil Response for Seismic-Loading Applications. Journal of Geotechnical and Geoenvironmental Engineering, 146(7), p.04020053.