A GENERALIZED GRADIENT SMOOTHING TECHNIQUE AND THE SMOOTHED BILINEAR FORM FOR GALERKIN FORMULATION OF A WIDE CLASS OF COMPUTATIONAL METHODS

By Guirong Liu. 2008

400 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/f36184b11290362e35d4844503188830096d95d0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

A node-based smoothed finite element method with stabilized discrete shear gap technique for analysis of Reissner–Mindlin plates (2010, neutral): “A general frameworkforthisstrainsmoothingtechniqueinFEMcanbefound in [40, 41 ].”
An edge-based smoothed tetrahedron finite element method (ES-T-FEM) for 3D static and dynamic problems (2013, methodology): “The strain smoothing technique was further extended to generalized gradient smoothing technique allowing the use of discontinuous functions [29] and weakened weak formulation [30].”
A novel shape function approach of dynamic load identification for the structures with interval uncertainty (2016, methodology): “The vertical dynamic displacement response of the joint 4 is used to identify the dynamic load, and it can be obtained through FEM under the midpoint of uncertain parameters.”
Meshfree Methods: Progress Made after 20 Years (2017, positive): “Various nodal and element strain smoothing techniques have been proposed by Liu et al. for finite elements, and are termed the smoothed finite-element meth-ods (Liu and Nguyen-Thoi 2010; Liu 2008; Liu et al. 2007a).”
A face‐based smoothed finite element method (FS‐FEM) for 3D linear and geometrically non‐linear solid mechanics problems using 4‐node tetrahedral elements (2009, methodology): “Liu [8] has applied this technique and extended it to a generalized gradient smoothing technique allowing the use of discontinuous functions.”
A novel computational inverse technique for load identification using the shape function method of moving least square fitting (2014, methodology): “In this paper, in order to resolve the contradiction above, a novel method is proposed to identify dynamic load in time domain according to the thought of discretized field variables by the finite element method (FEM) [26].”
A node-based smoothed finite element method (NS-FEM) for upper bound solutions to solid mechanics problems (2009, methodology): “The foundation of the LC-PIM is based on the generalized smoothed gradient smoothing technique [31].”
A G space theory and a weakened weak (W2) form for a unified formulation of compatible and incompatible methods: Part I theory (2010, methodology): “Using the smoothing technique and the generalized smoothing technique that works also for discontinuous functions [22], we defined the ‘smoothed’ strain as (Figure 1)”
A Smoothed Finite Element Method (SFEM) for Linear and Geometrically Nonlinear Analysis of Plates and Shells (2008, background): “The properties of the smoothed Galerkin weak form are examined and proven by Liu (2008).”