A linear smoothed meshfree method with intrinsic enrichment functions for 2D crack analysis

Abstract

PurposeThis article aims to develop an accurate and efficient meshfree Galerkin method based on the strain smoothing technique for linear elastic continuous and fracture problems.Design/methodology/approachThis paper proposed a generalized linear smoothed meshfree method (LSMM), in which the compatible strain is reconstructed by the linear smoothed strains. Based on the idea of the weighted residual method and employing three linearly independent weight functions, the linear smoothed strains can be created easily in a smoothing domain. Using various types of basic functions, LSMM can solve the linear elastic continuous and fracture problems in a unified way.FindingsOn the one hand, the LSMM inherits the properties of high efficiency and stability from the stabilized conforming nodal integration (SCNI). On the other hand, the LSMM is more accurate than the SCNI, because it can produce continuous strains instead of the piece-wise strains obtained by SCNI. Those excellent performances ensure that the LSMM has the capability to precisely track the crack propagation problems. Several numerical examples are investigated to verify the accurate, convergence rate and robustness of the present LSMM.Originality/valueThis study provides an accurate and efficient meshfree method for simulating crack growth.

An adaptive extended finite element based crack propagation analysis method

“…In engineering structures, the existence of cracks will reduce strength and life, causing serious safety accidents and economic losses. In recent years, with the rapid development of computational science, computational mechanics is widely used in crack analysis, including finite element method (FEM) [1][2][3], meshless methods (MMs) [4][5][6], boundary element method (BEM) [7][8][9][10], XFEM [11][12][13], etc. However, the traditional finite element method relies too much on the mesh, which leads to the complexity of the pre-processing of crack growth.…”