Specifications

1 School of Civil Engineering and Architecture, Xi'an University of Technology, Xi'an 710048,
China
2 School of Mathematics and Computer Science, Ningxia University, Ningxia 750021, China
Corresponding author: Ma, W.-T. ([e-mail])
Source title: Yantu Lixue/Rock and Soil Mechanics
Abbreviated source title: Rock Soil Mech
Volume: 33
Issue: 11
Issue date: November 2012
Publication year: 2012
Pages: 3447-3453
Language: Chinese
ISSN: 10007598
Document type: Journal article (JA)
Publisher: Academia Sinica, Wuhan, 430071, China
Abstract: A new method which couples the level set method with meshless method to
simulate crack growth is presented. The coupling of level set and meshless method can achieve
naturally because they all set up based on the discrete nodal data. Two level sets that are
orthogonal to one another at the crack tip are used to represent the geometry of crack and the
location of crack tip, and to construct the Heaviside skip function and the Westergaard enriched
function near the crack tip in the element-free Galerkin method (EFGM) discontinuous
approximation. New crack tips are defined by the update algorithm of level set easily when the
crack is growing. The coupling method does not use the visibility method, the diffraction method
or the transparency method. The √r singularity is reproduced very well; and the convergence
for elastic problems is improved. The passage of crack has no influence on the nodal domain.
Smaller domain is used to calculation, which keeps the band and sparsity of the over all stiffness
matrix. In addition, the level set makes the selection of enriched nodes and the establishment of
additional function simply; and its update process needs no evolution equations. The numerical
results show that the presented method has higher computational accuracy; and the simulated
expanding path of crack is coincided with the tested curve. So, the results verify the validity and
accuracy of the presented method.
Number of references: 17
Main heading: Numerical methods
Controlled terms: Computational mechanics - Crack propagation - Crack tips -
Cracks - Drop breakup - Level measurement - Orthogonal functions - Stiffness
matrix
Uncontrolled terms: Computational accuracy - Coupling methods - Diffraction
methods - Discontinuous approximation - Elastic problems - Element-free Galerkin
method - Evolution equations - Heaviside - Level Set - Level Set method -
Mesh-less methods - Nodal domain - Numerical results - Process needs
Classification code: 421 Strength of Building Materials; Mechanical Properties - 921
Mathematics - 921.6 Numerical Methods - 931.2 Physical Properties of Gases, Liquids and
Solids - 943.2 Mechanical Variables Measurements
Database: Compendex