Convergence and stabilization of stress‐point integration in mesh‐free and particle methods

By Thomas-Peter Fries, Ted Belytschko. 2008

65 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/c21e57dc8369575c6d84eb14e57577ead19522b1

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

Aspects of the use of orthogonal basis functions in the element‐free Galerkin method (2009, background): “Reference [14] mentions the importance of nodal arrangements but only insofar as they affect the integration necessary for the weak form, again not the problem that we highlight here.”
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].”
Enhancement of stability and accuracy of the moving particle semi-implicit method (2011, background): “However, apart from the increased complexity of mathematical formulations, in case of application of stress points, the stability and convergence would depend on the distribution of particles in the domain, where a poor convergence rate would be obtained for irregular particle distributions [18].”
Meshfree Methods: Progress Made after 20 Years (2017, unknown): “However, this method does require additional techniques such as residual-based stabilization in order to ensure convergent and stable solutions in all situations (Fries and Belytschko 2008).”
Second‐order accurate derivatives and integration schemes for meshfree methods (2012, background): “DOI: 10.1002/nme.4359 Second-order accurate derivatives and integration schemes for meshfree methods Qinglin Duan1,*,†, Xikui Li1,2, Hongwu Zhang1,2 and Ted Belytschko3 1Department of Engineering Mechanics, Dalian University of Technology, Dalian, Liaoning 116024, China 2The State Key Laboratory of ”
Consistent element‐free Galerkin method (2014, background): “However, the convergence of such a method is not good, and a mild oscillation still could happen [29].”
Current achievements and future perspectives for projection-based particle methods with applications in ocean engineering (2016, background): “…the increased complexity of mathematical formulations, in case of application of stress points, the stability and convergencewould depend on the distribution of particles in the domain, where a poor convergence rate would be obtained for irregular particle distributions (Fries and Belytschko 2008).”
An accelerated, convergent, and stable nodal integration in Galerkin meshfree methods for linear and nonlinear mechanics (2016, methodology): “Stress points have also been utilized to avoid the instability [21, 22], but this technique requires additional stabilization such as least-squares to ensure stability and accuracy [31].”
Adaptive element-free Galerkin method applied to the limit analysis of plates (2010, methodology): “In the framework of meshfree methods, it is advantageous if the problem under consideration can be solved by evaluating quantities at the nodes only [26–32].”
A new support integration scheme for the weakform in mesh‐free methods (2010, background): “Fries and Belytschko [18] analyzed stress point quadrature for the Laplace equation.”