What is a reference for the particle method you are trying to implement? From the previous discussion it does not seem that a classical FE form is the best format for the development. How are quadrature points related to the particles involved? As Professor Govindjee mentioned a uformfe structure related to particles may be better.
Hello Professor Taylor,
For added background, I am a first year PhD student studying computational mechanics at UCSD under Professor JS Chen and am familiar with FEAP 7.4 from when I took CE 233 as a ME undergraduate at UCB.
Regarding references: I would recommend checking out,
Meshfree and Particle Methods : Fundamentals and Applications. Specifically the following sections:
- Ch.5 Deals with the shape function construction for the Reproducing Kernel Particle Method.
- Ch.6.2 Deals with Gauss Quadrature as an introductory scheme for domain integration.
- Ch.10 Deals with an existing 2D implementation of the core particle method based in Matlab by a past graduate student.
Currently I am just working on implementing one of the simplest RKPM schemes in FEAP, see Ch.6.2, as an academic exercise.
Regarding quadrature points: RK shape functions are global, with each node having its own support size based off of its proximity to neighboring nodes. For integration over a domain, if the point being evaluated for a given integration scheme exists within a neighboring nodes support, then that nodes shape function will have a non-zero contribution during integration regardless of whether the node exists within the bounds of the domain being integrated. This is talked about in Ch.6 as one of the simplest schemes to incorporate with traditional FEM, though other schemes are discussed in later sections. (See Figure 6.4)
It would appear that uformfe.f is not included in my copy of FEAPpv. Is this exclusive to the full FEAP program?
References:
Belytschko, T., Chen, J.-S., & Hillman, M. C. (2024).
Meshfree and particle methods : fundamentals and applications. Wiley.