A three-node triangular element fitted to numerical manifold method with continuous nodal stress for crack analysis

2016 ◽  
Vol 162 ◽  
pp. 51-75 ◽  
Author(s):  
Yongtao Yang ◽  
Hong Zheng
Keyword(s):  
Triangular Element ◽  
Numerical Manifold Method ◽  
Crack Analysis ◽  
Numerical Manifold

MLS based local approximation in numerical manifold method

2018 ◽  
Vol 35 (7) ◽  
pp. 2429-2458
Author(s):  
Yuanqiang Chen ◽  
H. Zheng ◽  
Wei Li ◽  
Shan Lin
Keyword(s):  
Interpolation Method ◽  
Partition Of Unity ◽  
Local Approximation ◽  
Least Square ◽  
Triangular Element ◽  
Numerical Manifold Method ◽  
Content Type ◽  
Moving Least Square ◽  
The Individual ◽  
Numerical Manifold

Purpose The purpose of this paper is to propose a new three-node triangular element in the framework of the numerical manifold method (NMM), which is designated by Trig3-MLScns. Design/methodology/approach The formulation uses the improved parametric shape functions of classical triangular elements (Trig3-0) to construct the partition of unity (PU) and the moving least square (MLS) interpolation method to construct the local approximation function. Findings Compared with the classical three-node element (Trig3-0), the Trig3-MLScns element has a higher order of approximations, much better accuracy and continuous nodal stress. Moreover, the linear dependence problem associated with many PU-based methods with high-order approximations is eliminated in the present element. A number of numerical examples indicate the high accuracy and robustness of the Trig3-MLScns element. Originality/value The proposed element inherits the individual merits of the NMM and the MLS.

scholarly journals Time-dependent deformation and failure of granite based on the virtual crack incorporated numerical manifold method

2021 ◽  
Vol 133 ◽  
pp. 104070
Author(s):  
Xian-yang Yu ◽  
Tao Xu ◽  
Michael J. Heap ◽  
Patrick Baud ◽  
Thierry Reuschlé ◽  
...  
Keyword(s):  
Time Dependent ◽  
Numerical Manifold Method ◽  
Deformation And Failure ◽  
Numerical Manifold
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