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Meshfree methods

About: Meshfree methods is a research topic. Over the lifetime, 2216 publications have been published within this topic receiving 69596 citations.


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TL;DR: In this article, a floating stress-point integration mesh-free method for large deformation analysis of elastic and elastoplastic materials is proposed, which is a Galerkin mesh free method with an updated Lagrangian procedure and a quasi-implicit time-advancing scheme.
Abstract: SUMMARY A new meshfree formulation of stress-point integration, called the floating stress-point integration meshfree method, is proposed for the large deformation analysis of elastic and elastoplastic materials. This method is a Galerkin meshfree method with an updated Lagrangian procedure and a quasi-implicit time-advancing scheme without any background cell for domain integration. Its new formulation is based on incremental equilibrium equations derived from the incremental virtual work equation, which is not generally used in meshfree formulations. Hence, this technique allows the temporal continuity of the mechanical equilibrium to be naturally achieved. The details of the new formulation and several examples of the large deformation analysis of elastic and elastoplastic materials are presented to show the validity and accuracy of the proposed method in comparison with those of the finite element method. Copyright © 2012 John Wiley & Sons, Ltd.

6 citations

Journal ArticleDOI
TL;DR: In this paper, a mesh-free Galerkin method for the solution of Reissner-Mindlin plate problems is proposed, which is written in terms of the primitive variables only (i.e., rotations and transverse displacement).

6 citations

Journal ArticleDOI
TL;DR: In this paper, a convex mesh-free framework for solving the scalar Helmholtz equation in the waveguide analysis of electromagnetic problems is presented, which exhibits a weak Kronecker-delta property at waveguide boundary and allows a direct enforcement of homogenous Dirichlet boundary conditions for the transverse magnetic (TM) mode analyses.
Abstract: This paper presents a convex meshfree framework for solving the scalar Helmholtz equation in the waveguide analysis of electromagnetic problems. The generalized meshfree approximation (GMF) method using inverse tangent basis functions and cubic spline weight functions is employed to construct the flrst-order convex approximation which exhibits a weak Kronecker-delta property at the waveguide boundary and allows a direct enforcement of homogenous Dirichlet boundary conditions for the transverse magnetic (TM) mode analyses. Four arbitrary waveguide examples are analyzed to demonstrate the accuracy of the presented formulation, and comparison is made with the analytical, flnite element and meshfree solutions.

6 citations

Journal ArticleDOI
TL;DR: The aim of this paper is to present a mesh generation approach using the application of self-organizing artificial neural networks through adaptive finite element computations, which seems naturally extendible to quadrilateral elements.

6 citations

Journal ArticleDOI
TL;DR: A novel error estimation procedure is presented that is based on the enhanced assumed strain (EAS) method and applied to the reproducing kernel particle method (RKPM) as a representative of Galerkin meshfree methods.
Abstract: Gradient averaging-type a posteriori error estimators applied to the finite element method enjoy great popularity in the engineering community. This is mainly because they are easy in their construction and computer implementation and usually provide constant-free and sharp error estimates on the expense of losing the bounding property. However, it proves difficult to transfer this error estimation procedure to Galerkin meshfree methods. One reason is that the meshfree gradient approximation is generally rather accurate per se and difficult to improve. Moreover, in many Galerkin meshfree methods the shape functions are no interpolants, as required in the original idea of constructing the recovered and thus smooth gradient field. In this paper, a novel error estimation procedure is presented that is based on the enhanced assumed strain (EAS) method and applied to the reproducing kernel particle method (RKPM) as a representative of Galerkin meshfree methods. The error estimator is naturally tailored to Galerkin meshfree methods if stabilized conforming nodal integration (SCNI) is employed, which provides two gradient fields: a globally smooth one (the compatible strain) and a cellwise constant one (the enhanced assumed strain). It is shown that the difference (the enhanced strain) can be used to derive an error estimator that follows the notion of gradient averaging-type error estimators and resolves its issues when applied to Galerkin meshfree methods. In addition, the enhanced-strain error estimator is even easier to implement and computationally less expensive than gradient averaging-type error estimators. Numerical examples of engineering interest illustrate the performance of the enhanced-strain error estimator presented in this paper.

6 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202355
2022112
2021102
202092
201996
201897