Meshfree methods

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

A Meshfree procedure for the microscopic analysis of particle-reinforced rubber compounds

Abstract: This paper presents a meshfree procedure using a convex generalized meshfree (GMF) approximation for the large deformation analysis of particle-reinforced rubber compounds on microscopic level. The convex GMF approximation possesses the weak-Kronecker-delta property that guarantees the continuity of displacement across the material interface in the rubber compounds. The convex approximation also ensures the positive mass in the discrete system and is less sensitive to the meshfree nodal support size and integration order effects. In this study, the convex approximation is generated in the GMF method by choosing the positive and monotonic increasing basis function. In order to impose the periodic boundary condition in the unit cell method for the microscopic analysis, a singular kernel is introduced on the periodic boundary nodes in the construction of GMF approximation. The periodic boundary condition is solved by the transformation method in both explicit and implicit analyses. To simulate the interface de-bonding phenomena in the rubber compound, the cohesive interface element method is employed in corporation with meshfree method in this study. Several numerical examples are presented to demonstrate the effectiveness of the proposed numerical procedure in the large deformation analysis.

Meshless local Petrov-Galerkin method with radial basis functions applied to electromagnetics

Abstract: Meshless methods are a new class of numerical techniques for solving partial differential equations and have attracted considerable attention in computational mechanics in recent years. Owing to the ‘mesh-free’ characteristic, these methods offer some advantages over the conventional mesh-based finite-element techniques. A formulation for the meshless local Petrov–Galerkin method is described and its application to electromagnetic modelling investigated.

An edge‐based smoothed finite element method (ES‐FEM) using 3‐node triangular elements for 3D non‐linear analysis of spatial membrane structures

Abstract: An edge-based smoothed finite element method using 3-node triangular membrane elements (ES-FEM-T3) is proposed to analyze three-dimensional (3D) spatial membrane structures under large deflection, rotation, and strain. In our 3D formulation, co-rotational local coordinate systems associated with the edge-based smoothing domains are constructed. Edge-based gradient smoothing for the spatial membrane structure is performed in global Cartesian coordinate system and transformed into the co-rotational local coordinate system. The smoothed strain and stress can then be properly evaluated in the co-rotational local coordinate system after the elimination of the rigid body motions simply by coordinates transformation. Explicit time integration scheme is used to compute the transient response of the 3D spatial membrane structure to time-domain excitations, and the dynamic relaxation method is employed to obtain steady-state solutions. The numerical results demonstrate that the proposed method produces much better solution accuracy and computational efficiency than the standard FEM using T3 membrane element. Copyright © 2010 John Wiley & Sons, Ltd.