Meshfree methods

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

Particle Methods for Viscous Flows: Analogies and Differences Between the SPH and DVH Methods

Abstract: In this work two particle methods are studied in the context of viscous flows. The first one is a Vortex Particle Method, called Diffused Vortex Hydrodynamics (DVH), recently developed to simulate complex viscous flows at medium and high Reynolds regimes. This method presents some similarities with the SPH model and its Lagrangian meshless nature, even if it is based on a different numerical approach. Advantages and drawbacks of the two methods have been previously studied in Colagrossi et al. [1] from a theoretical point of view and in Rossi et al. [2], where these particle methods have been tested on selected benchmarks. Further investigations are presented in this article highlighting analogies and differences between the two particle models.

Evaluation of fracture parameters for crack problems in fgm by a meshless method

Abstract: A meshless method based on the local Petrov-Galerkin approach is proposed for crack analysis in two-dimensional (2D), anisotropic and linear elastic solids with continuously varying material properties. Both quasi-static thermal and transient elastodynamic problems are considered. For time-dependent problems, the Laplace transform technique is utilized. The analyzed domain is divided into small subdomains of circular shapes. A unit step function is used as the test function in the local weak form. It leads to Local Integral Equations (LIE) involving a domain-integral only in the case of transient dynamic problems. The Moving Least Squares (MLS) method is adopted for approximating the physical quantities in the LIE. Efficient numerical methods are presented to compute the fracture parameters, namely, the stress intensity factors and the $ T$-stress, for a crack in Functionally Graded Materials (FGM). The path-independent integral representations for stress intensity f actors and $ T$-stresses in continuously non-homogeneous FGM are presented.

Treatment of near-incompressibility in meshfree and immersed-particle methods

Abstract: We propose new projection methods for treating near-incompressibility in small and large deformation elasticity and plasticity within the framework of particle and meshfree methods. Using the $$\overline{\mathbf {B}}$$ and $$\overline{\mathbf {F}}$$ techniques as our point of departure, we develop projection methods for the conforming reproducing kernel method and the immersed-particle or material point-like methods. The methods are based on the projection of the dilatational part of the appropriate measure of deformation onto lower-dimensional approximation spaces, according to the traditional $$\overline{\mathbf {B}}$$ and $$\overline{\mathbf {F}}$$ approaches, but tailored to meshfree and particle methods. The presented numerical examples exhibit reduced stress oscillations and are free of volumetric locking and hourglassing phenomena.