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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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Journal ArticleDOI
TL;DR: A theoretical analysis of super-convergence in Sobolev norms for reproducing kernel (RK) approximations when the interpolation order p is even is provided, and the concept of pseudo-super-conversgence is introduced to explain why in practice the super- Convergence phenomenon is sometimes observed for general cases.

10 citations

Journal ArticleDOI
TL;DR: In this article, a matching field strategy is adopted by using the element free Galerkin method in which shape functions of the longitudinal displacement fields are obtained from the derivatives of shape function of the transverse displacement fields.
Abstract: In the numerical analysis of composite beam-columns inconsistencies in the shape functions of the transverse and longitudinal displacement fields may cause oscillations in the slip field and reduction in the accuracy of the results known as slip-locking which is typical of multi-field problems of this type. In order to eliminate slip-locking, matching field strategy is adopted herein by using the element free Galerkin method in which shape functions of the longitudinal displacement fields are obtained from the derivatives of shape functions of the transverse displacement fields. Continuous blending method is modified in order to couple element-free Galerkin and finite element methods when the matching field approach is used in the meshfree region. This modification allows for direct assembly of the stiffness matrices that are built for separate finite element and meshfree regions, the boundary conditions can be directly applied and the reaction forces can also be calculated directly from the structural stiffness matrix.

10 citations

Journal ArticleDOI
TL;DR: Oh et al. as discussed by the authors developed mesh-free reproducing polynomial particle shape functions, patchwise RPP and reproducing singularity particle (RSP) shape functions with use of flat-top partition of unity.
Abstract: Since meshless methods have been introduced to alleviate the difficulties arising in conventional finite element method, many papers on applications of meshless methods to boundary element method have been published. However, most of these papers use moving least squares approximation functions that have difficulties in prescribing essential boundary conditions. Recently, in order to strengthen the effectiveness of meshless methods, Oh et al. developed meshfree reproducing polynomial particle (RPP) shape functions, patchwise RPP and reproducing singularity particle (RSP) shape functions with use of flat-top partition of unity. All of these approximation functions satisfy the Kronecker delta property. In this paper, we report that meshfree RPP shape functions, patchwise RPP shape functions, and patchwise RSP shape functions effectively handle boundary integral equations with (or without) domain singularities.

10 citations

Journal ArticleDOI
TL;DR: In this paper, an adaptive node regeneration method is proposed for solving elasticity problems using the mixed discrete least squares meshless (MDLSM) method, which starts with a point-wise error estimation of the solution produced on an arbitrary initial configuration defined by the user using the MDLSM method.
Abstract: An efficient adaptive node regeneration method is proposed in this paper for solving elasticity problems using the mixed discrete least squares meshless (MDLSM) method. The method starts with a point-wise error estimation of the solution produced on an arbitrary initial configuration defined by the user using the MDLSM method. The point-wise error estimate is associated with the support domain of the nodal points and used to calculate the required nodal spacing at each support domain and subsequently generate new nodes at support domain level. A node-removing process is then used to remove some of the nodes created at the overlapping regions of the support domains. To improve the quality of the final configuration, a node-moving procedure based on interpolation of the errors on the original configuration is used to create the final nodal configuration. The proposed method is a single step refinement procedure and is capable of producing nodal configurations of desired accuracy for different problems. The proposed method is used to simulate three benchmark examples from the literature and the results are produced and compared with those of the conventional multi-stage node enrichment method. The results indicate the superior efficiency and effectiveness of the proposed method compared to the available methods.

10 citations

Book ChapterDOI
01 Jan 2005
TL;DR: In this paper, the authors compared Petrov-Galerkin methods with mesh-free stabilised methods for the solution of the Navier-Stokes equations in Eulerian formulation and found that reliable and successful approximation with standard formulas for the stabilisation parameter can only be expected for shape functions with small supports or dilatation parameters.
Abstract: Meshfree stabilised methods are employed and compared for the solution of the incompressible Navier-Stokes equations in Eulerian formulation. These Petrov-Galerkin methods are standard tools in the FEM context, and can be used for meshfree methods as well. However, the choice of the stabilisation parameter has to be reconsidered. We find that reliable and successful approximation with standard formulas for the stabilisation parameter can only be expected for shape functions with small supports or dilatation parameters.

10 citations


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