Stabilized conforming nodal integration in the natural‐element method

By Jeonghoon Yoo, Brian Moran, Jiun-Shyan Chen. 2004

187 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/b882820939dcb4a12959eb21131f6544037b78b3

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM) (2011, background): “where is a smoothing function that generally satisfies the following properties [19] (See Figure 2):”
An edge-based smoothed finite element method for visco-elastoplastic analyses of 2D solids using triangular mesh (2009, methodology): “The strain smoothing technique [4] has been proposed to stabilize the solutions in the context of the meshfree method and then applied in the natural element method [31].”
Adaptive analysis using the node‐based smoothed finite element method (NS‐FEM) (2011, methodology): “[18] to stabilize the solutions in the context of the meshfree method and then applied in the natural-element method [19].”
Meshfree and finite element nodal integration methods (2008, methodology): “A modification of the SCNI [1, 3] integration scheme is proposed and a gradient-based stabilization is proposed for the nodal strain method.”
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.”
Theoretical aspects of the smoothed finite element method (SFEM) (2007, methodology): “then extended the stabilized nodal integration to the natural-element method and solved the nearly incompressible problems without any modification of integration scheme [6].”
A node-based smoothed finite element method (NS-FEM) for upper bound solutions to solid mechanics problems (2009, methodology): “[14] to stabilize the solutions in the context of the meshfree method and then applied in the natural element method [15].”
Strain Smoothing for Stabilization and Regularization of Galerkin Meshfree Methods (2007, background): “[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 edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses of solids (2009, methodology): “[1] to stabilize the solutions in the nodal integrated meshfree methods and then applied to the natural element method [2].”
A smoothed finite element method for plate analysis (2008, unknown): “The SCNI approach was originally developed in meshfree methods as a normalization for nodal integration [17, 60] of the meshfree Galerkin weak form and recently in the FEM [38].”
An edge-based smoothed finite element method (ES-FEM) for analyzing three-dimensional acoustic problems (2009, methodology): “[10] to stabilize the solutions of nodal integrated meshfree methods and also in the natural-element method [11].”
Virtual and smoothed finite elements: A connection and its application to polygonal/polyhedral finite element methods (2015, background): “where ˆ is a smoothing function that generally satisfies the following properties [52] ˆ > 0 and Z”
Locking‐free continuum displacement finite elements with nodal integration (2008, methodology): “The present technique is also close to the so-called stabilized conforming nodal integration as used in various mesh free methods: see References [3, 21, 20, 16].”
Stabilized and variationally consistent nodal integration for meshfree modeling of impact problems (2014, methodology): “SCNI has been applied to other meshfree methods [25] and has also been extended to plates and shells [7,22,23].”
ADDITIONAL PROPERTIES OF THE NODE-BASED SMOOTHED FINITE ELEMENT METHOD (NS-FEM) FOR SOLID MECHANICS PROBLEMS (2009, methodology): “…methods, Liu et al. have applied and extended the strain smoothing technique used in the nodal integrated meshfree methods [Chen et al. (2001); Yoo et al. (2004)] to formulate the linear conforming point interpolation method (LC-PIM or NS-PIM) [Liu et al. (2005)] and the linearly conforming…”