Meshfree methods

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

Least-squares meshfree collocation method

Abstract: A least-squares meshfree collocation method is presented The method is based on the first-order differential equations in order to result in a better conditioned linear algebraic equations, and to obtain the primary variables (displacements) and the dual variables (stresses) simultaneously with the same accuracy The moving least-squares approximation is employed to construct the shape functions The sum of squared residuals of both differential equations and boundary conditions at nodal points is minimized The present method does not require any background mesh and additional evaluation points, and thus is a truly meshfree method Unlike other collocation methods, the present method does not involve derivative boundary conditions, therefore no stabilization terms are needed, and the resulting stiffness matrix is symmetric positive definite Numerical examples show that the proposed method possesses an optimal rate of convergence for both primary and dual variables, if the nodes are uniformly distributed However, the present method is sensitive to the choice of the influence length Numerical examples include one-dimensional diffusion and convection-diffusion problems, two-dimensional Poisson equation and linear elasticity problems

MLPG (Meshless Local Petrov-Galerkin method) for Heat Conduction Analysis on Welding Moving Heat Source Problem

Abstract: Recently, the technique of numerical simulations and the performance of computers are rapidly improved. Therefore, the structural analysis for welding phenomena based on thermal-elastic-plastic FEM can compute with good accuracy in short time. But, if the model to be analyzed is large such as ship structure and the shape is complex, they may cause the problem that preprocessing such as mesh division process consumes much time. To overcome these problems, mesh free method such as MLPG (Meshless Local Petrov-Galerkin Method) has been developed. MLPG is one of the complete meshless methods. This means that MLPG never use the element divisions. Therefore, the connectibility information between nodes and elements is not necessary and preprocessing time expected to be reduced. Accordingly, MLPG is considered as one of the next generation computational methods which may be alternative method of FEM.Then, in order to develop structural analysis for welding problem, Meshless Local Petrov-Galerkin method (MLPG) for heat conduction analysis is applied for the moving heat source problem of welding in this study. The validity, applicability and fundamental characteristics of MLPG which is used in this study are verified through the application of bead-on-plate.Finally, the adaptive method for MLPG including generation and elimination of nodal points is proposed.

Enriched Finite Element and Meshfree Methods for Dynamic Crack Propagation Problems

Abstract: Extended meshfree methods for dynamic crack propagation are reviewed. One class of methods enforces crack path continuity while the other class of method treats the crack as set of cracked particles. In the first method, crack path continuity is enforced either by use of a crack tip enrichment or by use of Lagrange multipliers. All methods are implemented in two and three dimensions and are compared to experimental results.

Numerically simulating structural behaviors of embedded bi-materials using meshfree method

Abstract: Methods and systems for numerically simulating structural behaviors of embedded bi-materials are disclosed. At least first and second grid models are created independently for an embedded bi-material that contains an immersed material embedded entirely within a base material. First group of meshfree nodes represents the entire domain (i.e., base plus immersed materials). Second group of meshfree nodes represents the immersed or embedded material, which includes all interface nodes and nodes located within a space bordered by the material interface. Numerical structural behaviors of the embedded bi-material are simulated using the first and second set of meshfree nodes with a meshfree method that combines two meshfree approximations. The first meshfree approximation covers the first set of meshfree nodes and is based on properties of the base material, while the second meshfree approximation covers the second set of meshfree nodes and is based on a differential between the immersed and base materials.

Graphical Interface for Electromagnetic Problem Solving Using Meshless Methods

Abstract: It is common to find a software with a graphical interface that uses the finite element method or the finite difference method to solve electromagnetic problems. However, there are just few software which use meshless methods to solve these problems, and none with a graphical interface. This project aims at developing a graphical software capable of solving Electromagnetic Problems by meshless methods. Among these meshless methods, it is possible to mention the Element Free Galerkin Method (EFG), Meshless Local Petrov Galerkin (MLPG) and Point Interpolation Methods (PIM). The main idea is to enable the user to design the geometry of a problem, choose materials in the domain, impose boundary conditions to choose a meshless method to obtain a solution and view the results in a graphical form. This software-user interaction will be intermediated in the domain by a graphical user interface that makes transparent the using of the meshless method using an intuitive toolkit responsible for the problem design and for the solution visualization.