Second‐order accurate derivatives and integration schemes for meshfree methods

By Q. Duan, Xikui Li, Hongwu W. Zhang, Ted Belytschko. 2012

105 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/b3f549fe7397bb4a9e91080052f8dfbc791e29a1

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

An arbitrary order variationally consistent integration for Galerkin meshfree methods (2013, background): “[26] extended the linear exactness of SCNI to quadratic exactness by solving for the shape function derivatives at each integration point.”
Quadratic maximum-entropy serendipity shape functions for arbitrary planar polygons (2013, methodology): “    , (30) where {xl, xm, xn} are the three integration points (with equal weights) within the subtriangle, and this choice ensures that the matrix on the lefthand side is invertible [38].”
Meshfree Methods: Progress Made after 20 Years (2017, unknown): “More recently, an extension of SCNI for quadratic basis functions has been proposed (Duan et al. 2012).”
An accelerated, convergent, and stable nodal integration in Galerkin meshfree methods for linear and nonlinear mechanics (2016, methodology): “This method was later extended in [34, 35] to higher order schemes, which also have been shown to be very effective when compared to standard integration techniques.”
Consistent element‐free Galerkin method (2014, methodology): “in [20], except that the corrected nodal derivatives naturally present on the left-hand side of the equation with the development given here.”
Stabilized and variationally consistent nodal integration for meshfree modeling of impact problems (2014, methodology): “More recently, similar assumed strain constructions have been proposed for second order variationally consistency in [13].”
A displacement smoothing induced strain gradient stabilization for the meshfree Galerkin nodal integration method (2015, methodology): “The concept of integration constraint in SCNI method also has been generalized to achieve a quadratic consistent integration scheme [13].”