Stable particle methods based on Lagrangian kernels

By Timon Rabczuk, Ted Belytschko, Shaoping Xiao. 2004

492 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials, Safety, Risk, Reliability and Quality

View Paper: https://www.semanticscholar.org/paper/a16e5fe28e54e081a49bb479ca272c822161a503

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In Computational Mechanics

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Citations in the corpus

A simplified mesh‐free method for shear bands with cohesive surfaces (2007, methodology): “[28] for our construction of stress points.”
Analysis of functionally graded plates using an edge-based smoothed finite element method (2011, background): “One of major advantages of meshless approaches compared to FEM is capable of handling large deformations, nonlinear problems with moving discontinuities [32–35].”
Current achievements and future perspectives for projection-based particle methods with applications in ocean engineering (2016, background): “The problem related to the Lagrangian kernels is that they may not tolerate large deformations as in case of fluid flows (Belytschko and Xiao 2002; Rabczuk et al. 2004), particularly the violent ones.”
Enhancement of stability and accuracy of the moving particle semi-implicit method (2011, background): “The problem related to the Lagrangian kernels is that they may not tolerate large deformations as in case of fluid flows [5,59], particularly, the violent ones.”
A three-dimensional meshfree method for continuous multiple-crack initiation, propagation and junction in statics and dynamics (2007, unknown): “[45]; Belytschko et al.”
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].”
Isogeometric analysis : CAD, finite elements, NURBS, exact geometry and mesh refinement (2005, methodology): “For a state-of-the-art summary of meshless methods, see [23–40].”
Meshless methods: A review and computer implementation aspects (2008, methodology): “U N C O R R E C T E D P R O O F Please cite this article in press as: N.V. Phu, et al., Meshless methods: A review and computer implementation aspects, Math. methods is the smooth particle hydrodynamics (SPH) method by Lucy [77] and Gingold and Monaghan [54].”
Meshfree and finite element nodal integration methods (2008, background): “In lieu of stabilization, stress points [11, 12] are often introduced near the nodes to avoid these oscillations.”