Meshfree methods

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

A strong-form meshfree collocation method for modeling stationary cracks with frictional contact

Abstract: We present a strong-form meshfree collocation method for frictional contact of two deformable bodies within the context of frictional crack problems. The method inherently achieves desirable features of meshfree methods by completely avoiding the construction of meshes or grids, such that the only required numerical approximation units are nodes (used as collocation points). For the recognition of a contact or crack surface, a line segment is used without any connection with the node structure. A contact constraint due to two body frictional contact is implemented in the strong-form meshfree discretization. Since the contact boundary is a Neumann boundary, it contributes to the system of equations as a traction boundary condition, but it does not yield extra unknowns. Although the material is linear elastic, the presence of the constraint formulation leads to an iterative nonlinear solution procedure. The assembled discrete system generates a consistent and stable solution despite the presence of contact constraints and the crack discontinuity, because the constraint formulation and crack modeling are well combined with the strong-form meshfree collocation method. Numerical experiments demonstrate the robustness and consistency of the method through comparison with analytical and finite element solutions.

Dispersive Divergence-Free Vector Meshless Method for Time-Domain Analysis of Frequency-Dependent Media

Abstract: The dispersive meshless method with scalar basis function has been successfully applied for analysis of frequency dependent media. However, as scalar based meshless methods are not always divergence-free in the absence of source,inaccurate or even wrong solutions may be found in the results. To overcome this problem, in this paper, a new dispersive formulation of meshless method with vector basis function is proposed for analysis of dispersive materials. The divergence free property of this method improves the accuracy of simulation by eliminating the artificial charges generated due to the numerical analysis. Moreover, the frequency behavior of the dispersive medium is modeled using auxiliary-differential equations (ADE) method. The efficiency and divergence-free property of the proposed method are verified and compared with dispersive meshless method with scalar basis function by a numerical example.

The forward problem algorithm based on modified element free Galerkin method for bioluminescence tomography

Abstract: As an emerging and promising molecular imaging modality, bioluminescence tomography (BLT) can reconstruct the internal light source with the photon fluence on the small animal surface to reveal non-invasive molecular and cellular activities directly. In order to obtain higher precision and better spatial resolution in source reconstruction, the solution accuracy for the forward problem of BLT should be improved as high as possible. In this contribution, we present a modified element free Galerkin method (MEFGM) to calculate photon propagation in the biological tissue. This method is based on moving least squares (MLS) approximation which requires only a series of nodes in the region of interest, so complicated meshing task can be avoided compared with finite element method (FEM). Furthermore, MLS shape functions are further modified to satisfy the delta function property, which can simplify the processing of boundary conditions in comparison with traditional meshless methods. Finally, the numerical simulation experiments demonstrate the effectiveness and feasibility of this proposed method by comparing the solution of MEFGM with that of FEM.

Meshfree solution of tapered elastic bar using element free Galerkin method

Abstract: The aim of this paper is to give a practical view of meshfree methods based on the element free Galerkin (EFG) method, to students and beginners on the meshfree methods The methodology has been presented in very easy and lucid form to bring clarity and understanding without getting into the mesh of mathematical derivation and various words used to represent similar terms in the research environment The EFG method was selected for the purpose, being easy to implement and versatile The tapered bar subjected to point load is considered as an example, as it gives the blend of simplicity and complexity along with the easier derivation of the exact solution, which can be compared to the obtained meshfree solution The MATLAB code has been used to find the nodal displacement and stresses, and their plots along with exact solution and finite element method The code shall be made available to enthusiastic beginners and is expected to collaborate the findings

LOOCV-GRBFCM Performance Evaluation

Abstract: Finite element method (FEM) must be created the element mesh, it is very tedious and time-consuming. A novel meshless method doesn't require generating the element mesh, it reduces a large amount of computational and human time. The shape parameter plays a key role of meshless methods, the authors usually choose the shape parameter by trial and error or some other ad-hoc means. This study will propose LOOCV-GRBFCM to choose a "GOOD" shape parameter and solve problems automatically and practically. Performance evaluations will also be presented. We hope these results to support useful suggestions.