Topic
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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25 Nov 2009
TL;DR: In this article, the authors investigated the stabilized conforming nodal integration (SCNI) for metal-forming processes and found that the performance of SCNI is problem specific compared to a standard integration scheme.
Abstract: Meshless methods offer interesting properties for the simulation of bulk forming
processes. This research concerns the investigation of the stabilized conforming nodal integration scheme (SCNI) for use in metal-forming processes. Two tests are carried out. Firstly, the performance of SCNI is compared to a standard integration scheme. The performance seems problem specific. Secondly the footing of a piece of nearly incompressible material is used for testing the locking behavior of the method. No volumetric locking was found.
2 citations
TL;DR: An implicit time integration mesh-free collocation method for solving linear and nonlinear ODEs based on interpolating moving least squares technique, which uses singular weights for constructing ansatz functions, is presented in this paper.
Abstract: An implicit time integration meshfree collocation method for solving linear and nonlinear ordinary differential equations (ODEs) based on interpolating moving least squares technique, which uses singular weights for constructing ansatz functions, is presented. On an example of a system of equations for Foucault pendulum, the flexibility of the proposed approach is shown and the accuracy, convergence, and stability properties are investigated. In a nonlinear case, the method gives accurate results, which is demonstrated by the solution of Lorenz equations. The typical trajectory patterns, e.g. butterfly pattern, were observed and the properties of the method are compared to those of a higher-order time integration method.
2 citations
Journal Article•
TL;DR: In this paper, the basic principle of PIM and RPIM is introduced and numerical example shows that the new methods possess several advantages, such as high accuracy, high stability and high efficiency.
Abstract: A Point interpolation method which base on the basis function is a new meshless method. It is advantageous over the meshless methods based on moving least square (MLS) methods in implementation of esstionial boundary condition and over the original PIM with polynomial basis in avoiding singularity when shape functions are constructed. In this paper, the basic principle of PIM and RPIM is introduced. In addition, numerical example shows that the new methods possess several advantages, such as high accuracy, high stability and high efficiency. It is a promising method in engineering.
2 citations
TL;DR: In this article, a curvature-constructed method (CCM) for bending analysis of thin plates using three-node triangular cells and assumed piecewise linear deflection field is presented.
Abstract: This paper presents a curvature-constructed method (CCM) for bending analysis of thin plates using three-node triangular cells and assumed piecewisely linear deflection field. In the present CCM, the formulation is based on the classic thin plate theory, and only deflection field is treated as the field variable that is assumed piecewisely linear using a set of three-node triangular background cells. The slopes at nodes and/or the mid-edge points of the triangular cells are first obtained using the gradient smoothing techniques (GST) over different smoothing domains. Three schemes are devised to construct the curvature in each cell using these slopes at nodes and/or the mid-edge points. The generalized smoothed Galerkin weak form is then used to create the discretized system equations. The essential rotational boundary conditions are imposed in the process of constructing the curvature field, and the translational boundary conditions are imposed in the same way as in the standard FEM. A number of numerical examples, including both static and free vibration analyses, are studied using the present CCM and the numerical results are compared with the analytical ones and those in the published literatures. The results show that outstanding schemes can obtain very accurate solutions.
2 citations
TL;DR: In this article, a mesh-free multiscale method is presented for efficient analysis of solids with strain gradient plastic effects, where the scale decomposition is carried out based on variational form of the problem.
Abstract: A meshfree multiscale method is presented for efficient analysis of solids with strain gradient plastic effects In the analysis of strain gradient plastic solids, localization due to increased hardening of strain gradient effect appears Chen-Wang theory is adopted, as a strain gradient plasticity theory It represents strain gradient effects as an internal variable and retains the essential structure of classical plasticity theory In this work, the scale decomposition is carried out based on variational form of the problem Coarse scale is designed to represent global behavior and fine scale to represent local behavior and gradient effect by using the intrinsic length scale From the detection of high strain gradient region, fine scale region is adopted Each scale variable is approximated using meshfree method Meshfree approximation is well suited for adaptivity As a method of increasing resolution, partition of unity based extrinsic enrichment is used Each scale problem is solved iteratively The proposed method is applied to bending of a thin beam and bimaterial shear layer and micro-indentation problems Size effects can be effectively captured in the results of the analysis
2 citations