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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: A node-based error estimator is presented to avoid the influence of spurious oscillation on adaptive analysis, and the recovered nodal stress value is obtained from a reference solution using a double refinement technique.
Abstract: Meshless methods are suitable for adaptive analysis, as the nodes are unstructured, and can be added or deleted freely. However, the smooth shape functions may produce spurious oscillation away from the region containing error, which may result in addition of unnecessary nodes. In order to avoid the influence of spurious oscillation on adaptive analysis, a node-based error estimator is presented. The recovered nodal stress value is obtained from a reference solution using a double refinement technique. Numerical tests are presented illustrating the effectiveness of the proposed approach in the terms of the number and distribution of nodes compared with traditional approaches.
2 citations
04 Sep 2002
TL;DR: The results show that the optimization analysis with the RKPM is able to accommodate very large shape changes required in the optimization process without doing particle re-adaptation, and provides accurate solutions of the objective and constraint functions and their gradients, therefore facilitates a fast convergence of the gradient-based optimization algorithm.
Abstract: The Reproducing Kernel Particle Method (RKPM) is one of several so-called meshfree methods of structural analysis and has been applied in this paper to the gradient-based shape optimization of two-dimensional automotive components. As indicated by the term meshfree, no mesh is required, but rather a field of points, or particles, are distributed within the domain of the problem. Three standard linear examples are chosen to allow a comprehensive comparison between the optimization with the RKPM and the state-of-art optimization tool in Unigraphics Version 18 (UG V18). The results show that the optimization analysis with the RKPM is able to accommodate very large shape changes required in the optimization process without doing particle re-adaptation, and provides accurate solutions of the objective and constraint functions and their gradients, therefore facilitates a fast convergence of the gradient-based optimization algorithm.
2 citations
12 Aug 2014
2 citations
11 May 2011
TL;DR: Some unique numerical solutions of fluid and solid mechanics by employing FMM as well as the Enriched Free Mesh Method are reviewed, including compressible flow and sounding mechanism in air-reed instruments as applications to fluid mechanics.
Abstract: The free mesh method (FMM) is a kind of the meshless methods intended for particle-like finite element analysis of problems that are difficult to handle using global mesh generation, or a node-based finite element method that employs a local mesh generation technique and a node-by-node algorithm. The aim of the present paper is to review some unique numerical solutions of fluid and solid mechanics by employing FMM as well as the Enriched Free Mesh Method (EFMM), which is a new version of FMM, including compressible flow and sounding mechanism in air-reed instruments as applications to fluid mechanics, and automatic remeshing for slow crack growth, dynamic behavior of solid as well as large-scale Eigen-frequency of engine block as applications to solid mechanics.
2 citations
TL;DR: A general-purpose, two- dimensional grid generator is described that produces region triangularizations well suited to each of the aforementioned methods for the solution of two-dimensional-field boundary-value problems.
Abstract: Numerical techniques such as finite elements, generalized finite differences and moment method for the solution of two-dimensional-field boundary-value problems pose different constraints as far as the discretization of the solution domain is concerned. A general-purpose, two-dimensional grid generator is described that produces region triangularizations well suited to each of the aforementioned methods. The triangularization is based on the radial sweep algorithm, which was developed by A. Mirante and N. Weingarten (1982) for solving topological modeling problems. Some application results are presented. >
2 citations