A unified stability analysis of meshless particle methods

By Ted Belytschko, Yong-Ming Guo, Wing Kam Liu, Shaoping Xiao. 2000

438 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/9122e7334fbb8d49ec6a88662ad8536e817d8d72

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In Civil and Structural Engineering

In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

Enhancement of stability and accuracy of the moving particle semi-implicit method (2011, background): “[4] showed that although a careful implementation of stress points removes the zero-energy modes, it does not in general eliminate the tensile instability.”
An extended constitutive correspondence formulation of peridynamics based on nonlinear bond-strain measures (2014, background): “As is known, [19], numerical implementations of peridynamic correspondence formulations are mired with instabilities commonly attributed to artifacts in particle-based discretizations of continuum mechanics [22, 23].”
Cracking particles: a simplified meshfree method for arbitrary evolving cracks (2004, positive): “In the stress point integration procedure, another set of particles is added to the model to remove instabilities caused by the rank deficiency which appears in a pure nodal integration, see Reference [43] or [46].”
Meshfree and finite element nodal integration methods (2008, methodology): “[34] showed that the tensile instability is related to the change of slope of the shape function for uncorrected SPH-type kernels and that stress points [11] can preclude the rank instability but not necessarily the tensile instability.”
Current achievements and future perspectives for projection-based particle methods with applications in ocean engineering (2016, methodology): “(v) Lagrangian kernels As previously stated, although a careful implementation of stress points removes the zero-energy modes, it does not eliminate the tensile instability (Belytschko et al. 2000).”
Immersed particle method for fluid–structure interaction (2009, methodology): “The method uses a Lagrangian formulation for the fluid [17] that has been shown to be stable and does not suffer from the tensile instability noted in [18–20].”
A three dimensional large deformation meshfree method for arbitrary evolving cracks (2007, background): “[6] have shown previously that Eulerian kernels tend to exhibit spurious instabilities in stretching.”
Meshfree Methods: Progress Made after 20 Years (2017, positive): “The accuracy, tensile instability, and spatial instability of SPH have been examined (Belytschko et al. 2000; Liu et al. 1995b; Swegle et al. 1994, 1995), and formulations have been proposed to correct the deficiencies in SPH (Bonet and Kulasegaram 2000; Dilts 1999; Monaghan 2000; Randles and…”
Convergence and stabilization of stress‐point integration in mesh‐free and particle methods (2008, background): “In fact, stress points do not suppress tension instabilities, which are due to a rather anomalous description of the motion in SPH, see [16].”