Meshfree methods

About: Meshfree methods is a research topic. Over the lifetime, 2216 publications have been published within this topic receiving 69596 citations.

Hybrid particle methods in frictionless impact-contact problems

Abstract: The dual particle dynamic (DPD) methods which employ two sets of particles have been demonstrated to have better accuracy and stability than the co-locational particle methods, such as the smooth particle hydrodynamics (SPH). The hybrid particle method (HPM) is an extension of the DPD method. Besides the advantages of the DPD method, the HPM possesses features which better facilitate the simulation of large deformations. This paper presents the continued development of the HPM for the numerical solution of two-dimensional frictionless contact problems. The interface contact force algorithm which employs a modified kinematic constraints method is used to determine the contact tractions. In this method, both the impenetrability condition and the traction condition are simultaneously enforced. In the original kinematic constraints method, only the former condition is satisfied. A new formulation to find stress derivatives at stress-free corners by imposing stress-free boundary conditions is also developed. The results for 1-D and 2-D contact problems indicate good accuracy for the contact formulation as well as the corner treatment when compared to analytical solutions and explicit finite element results using the commercial code LS-DYNA. Copyright © 2004 John Wiley & Sons, Ltd.

A meshfree method and its applications to elasto-plastic problems

Abstract: Standard finite element approaches are still ineffective in handling extreme material deformation, such as cases of large deformations and moving discontinuities due to severe mesh distortion. Among meshfree methods developed to overcome the ineffectiveness, Reproducing Kernel Particle Method (RKPM) has demonstrated its great suitability for structural analysis. This paper presents applications of RKPM in elasto-plastic problems after a review of meshfree methods and an introduction to RKPM. A slope stability problem in geotechnical engineering is analyzed as an illustrative case. The corresponding numerical simulations are carried out on an SGI Onyx3900 supercomputer. Comparison of the RKPM and the FEM under identical condi- tions showed that the RKPM is more suitable for problems where there exists extremely large strain such as in the case of slope sliding.

The Optimal Transportation Meshfree Method for General Fluid Flows and Strongly Coupled Fluid-Structure Interaction Problems

Abstract: This thesis develops a novel meshfree numerical method for simulating general fluid flows. Drawing from concepts in optimal mass transport theory and in combination with the notion of material point sampling and meshfree interpolation, the optimal transport meshfree (OTM) method provides a rigorous mathematical framework for numerically simulating three-dimensional general fluid flows with general, and possibly moving boundaries (as in fluid-structure interaction simulations). Specifically, the proposed OTM method generalizes the Benamou-Brenier differential formulation of optimal mass transportation problems which leads to a multi-field variational characterization of general fluid flows including viscosity, equations of state and general geometries and boundary conditions. With the use of material point sampling in conjunction with local max-entropy shape functions, the OTM method leads to a meshfree formulation bearing a number of salient features. Compared with other meshfree methods that face significant challenges to enforce essential boundary conditions as well as couple to other methods, such as the finite element method, the OTM method provides a new paradigm in meshfree methods. The OTM method is numerically validated by simulating the classical Riemann benchmark example for Euler flow. Furthermore, in order to highlight the ability of the OTM to simulate Navier-Stokes flows within general, moving three-dimensional domains, and naturally couple with finite elements, an illustrative strongly coupled FSI example is simulated. This illustrative FSI example, consisting of a gas-inflated sphere impacting the ground, is simulated as a toy model of the final phase of NASA's landing scheme devised for Mars missions, where a network of airbags are deployed to dissipate the energy of impact.