A Review on Recent Contribution of Meshfree Methods to Structure and Fracture Mechanics Applications

Abstract

Meshfree methods are viewed as next generation computational techniques. With evident limitations of conventional grid based methods, like FEM, in dealing with problems of fracture mechanics, large deformation, and simulation of manufacturing processes, meshfree methods have gained much attention by researchers. A number of meshfree methods have been proposed till now for analyzing complex problems in various fields of engineering. Present work attempts to review recent developments and some earlier applications of well-known meshfree methods like EFG and MLPG to various types of structure mechanics and fracture mechanics applications like bending, buckling, free vibration analysis, sensitivity analysis and topology optimization, single and mixed mode crack problems, fatigue crack growth, and dynamic crack analysis and some typical applications like vibration of cracked structures, thermoelastic crack problems, and failure transition in impact problems. Due to complex nature of meshfree shape functions and evaluation of integrals in domain, meshless methods are computationally expensive as compared to conventional mesh based methods. Some improved versions of original meshfree methods and other techniques suggested by researchers to improve computational efficiency of meshfree methods are also reviewed here.

An inverse procedure for identification of loads applied to a fractured component using a meshfree method

“…To solve a linear-elastic fracture mechanics problem, various numerical methods can be employed, the most important of which are the finite element method (FEM), 34 the extended finite element method (XFEM), 35 the boundary element method (BEM), 36 and the meshfree methods. 37 In the present research, to automatically calculate the crack growth direction and update the geometry of the domain, the meshfree RPIM is used. To evaluate the domain integrals of Equation (1), the background decomposition method (BDM) 38 is employed which is very well suited for meshless methods.…”

“…To solve a linear‐elastic fracture mechanics problem, various numerical methods can be employed, the most important of which are the finite element method (FEM), 34 the extended finite element method (XFEM), 35 the boundary element method (BEM), 36 and the meshfree methods 37 …”

High Performance of Local Meshfree Method With Reduced Integration

“…In the domain of the body, loaded by a system of external distributed surface and body forces with densities denoted, respectively by ̅ , on the boundary Γ and , in the domain Ω, consider a statically admissible stress field , that is any stress field that satisfies equilibrium with the system of applied external forces which therefore satisfies , (1) in the domain Ω, with boundary conditions…”

“…Grid-based methods required high quality meshes to solve fracture mechanics problems with material discontinuity, large deformation where excessive mesh distortion takes place and other situations. The meshless methods were generated with the expectation of providing more adaptive, accurate and stable numerical solutions that can deal with problems where conventional methods are not suitable [1]. Generally, their formulation is based in the weighted-residual method [2].…”

A numerical model based on ALE formulation to predict crack propagation in sandwich structures

“…Moreover, the methodology needs a different number of kinematic variables for each node and thus the total number of mesh points may vary with the crack growth. Others methodologies based on Discrete Element Method (DEM) [13] or MeshFree Methods (MFMs) [14] have been formulated in the last decade, providing valid alternatives to study such problems. Methods based on Moving Mesh technique (MM) provide a feasible and sensible way to predict crack growth mechanisms in continuum media.…”