Non‐linear version of stabilized conforming nodal integration for Galerkin mesh‐free methods

By Jiun-Shyan Chen, Sangpil Yoon, Cheng‐Tang Wu. 2002

321 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/0a086ffedda0007ae38bf80cb0e1a0cae1b8c561

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

An arbitrary order variationally consistent integration for Galerkin meshfree methods (2013, background): “Methods such as stabilized conforming nodal integration [16, 23, 24, 31, 32] have been proposed that are specifically formulated to meet the integration constraints and therefore pass the associated patch tests.”
Locking-free stabilized conforming nodal integration for meshfree Mindlin-Reissner plate formulation (2004, unknown): “A stabilized conforming nodal integration (SCNI) has been proposed as a stabilization mechanism for nodal integration [6,7] of meshfree Galerkin weak form.”
Stabilized conforming nodal integration in the natural‐element method (2004, unknown): “The nodal deformation gradients are calculated using the non-local vector operator ∇̃ and the position vector x [25]: F̃L = ∇̃0x(XL, t) = ∑ I ∇̃0 I (XL)xI (t) (33)”
Strain Smoothing for Stabilization and Regularization of Galerkin Meshfree Methods (2007, background): “Chen et al. [5, 6 , 13, 14] proposed a conforming strain smoothing in a stabilized conforming nodal integration (SCNI) as a stabilization of rank instability in nodal integration, and as a mechanism to pass linear patch test.”
An accelerated, convergent, and stable nodal integration in Galerkin meshfree methods for linear and nonlinear mechanics (2016, methodology): “A stabilized conforming nodal integration (SCNI) has been proposed [15, 23, 32] where derivatives are not directly evaluated at nodes, which circumvents the instability without the use of any derivatives or additional sampling points.”
A displacement smoothing induced strain gradient stabilization for the meshfree Galerkin nodal integration method (2015, background): “, Tokyo, Japan to be very effective in reducing the volumetric locking and shear locking in solid and structural analyses [10,12,35].”
Quadrature for meshless methods (2008, background): “In spite of its importance, only a few papers ([6],[9],[ 10 ],[12],[11],[1],[8]) address it, and these concentrate mainly on implementational aspects.”
Stabilized and variationally consistent nodal integration for meshfree modeling of impact problems (2014, methodology): “The strain smoothing stabilized conforming nodal integration (SCNI) has been proposed [9,10] to ease the situation, where derivatives are not directly evaluated at nodes which avoids the instability, but still requires attention because of additional unstable modes which may become excited in certai”
A level set enhanced natural kernel contact algorithm for impact and penetration modeling (2015, methodology): “Stabilized non-conforming nodal integration (SNNI) Stabilized conforming nodal integration (SCNI) has been proposed [35, 36] as an alternative to Gauss integration in order to satisfy the linear integration constraint in the domain integration of Galerkin meshfree methods and to ameliorate rank inst”