Investigation of the Accuracy of the Numerical Manifold Method on n-Sided Regular Elements for Crack Problems

2012 ◽  
Vol 157-158 ◽  
pp. 1093-1096
Author(s):  
Hui Hua Zhang ◽  
Jia Xiang Yan
Keyword(s):  
Numerical Manifold Method ◽  
Quadrilateral Element ◽  
Regular Elements ◽  
Linear Elastic ◽  
Quadrilateral Elements ◽  
Crack Problems ◽  
Elastic Crack ◽  
Triangular Elements ◽  
Numerical Manifold ◽  
Better Than

The numerical manifold method (NMM) is a representative among different numerical methods for crack problems. Due to the independence of physical domain and the mathematical cover system, totally regular mathematical elements can be used in the NMM. In the present paper, the NMM is applied to solve 2-D linear elastic crack problems, together with the comparison study on the accuracy of n-sided regular mathematical elements, i.e., the triangular elements (n=3), the quadrilateral elements (n=4) and the hexagonal elements (n=6). Our numerical results show that among different elements, the regular hexagonal element is the best and the quadrilateral element is better than the triangular one.

Analysis of Crack Interaction Problem by the Numerical Manifold Method

2012 ◽  
Vol 446-449 ◽  
pp. 797-801 ◽  
Author(s):  
Hui Hua Zhang
Keyword(s):  
Numerical Manifold Method ◽  
Crack Interaction ◽  
Multiple Crack ◽  
Linear Elastic ◽  
Cover System ◽  
Crack Problems ◽  
Elastic Fracture ◽  
Numerical Manifold ◽  
Physical Boundary ◽  
Interaction Problem

Due to the use of mathematical cover system and physical cover system, the numerical manifold method (NMM) is very suitable for discontinuity problems, especially for multiple crack problems. In the NMM, the mathematical cover system is independent of the physical boundary, and in this case, fully regular mathematical elements can be used. In the present paper, the NMM, combined with the rectangular mathematical elements, is applied to solve crack interaction problems in the linear elastic fracture mechanics (LEFM). To verify the present method, a typical numerical example is investigated and the results agree well with the reference solutions.

scholarly journals Numerical Manifold Method for the Forced Vibration of Thin Plates during Bending

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Ding Jun ◽  
Chen Song ◽  
Wen Wei-Bin ◽  
Luo Shao-Ming ◽  
Huang Xia
Keyword(s):  
Dynamic Equation ◽  
Degrees Of Freedom ◽  
Solution Process ◽  
Thin Plates ◽  
Numerical Manifold Method ◽  
Bending Vibration ◽  
Linear Elastic ◽  
Spline Basis ◽  
Generalized Degrees Of Freedom ◽  
Numerical Manifold

A novel numerical manifold method was derived from the cubic B-spline basis function. The new interpolation function is characterized by high-order coordination at the boundary of a manifold element. The linear elastic-dynamic equation used to solve the bending vibration of thin plates was derived according to the principle of minimum instantaneous potential energy. The method for the initialization of the dynamic equation and its solution process were provided. Moreover, the analysis showed that the calculated stiffness matrix exhibited favorable performance. Numerical results showed that the generalized degrees of freedom were significantly fewer and that the calculation accuracy was higher for the manifold method than for the conventional finite element method.

Fracture Analysis in Orthotropic Thermoelasticity Using Extended Finite Element Method

2015 ◽  
Vol 7 (6) ◽  
pp. 780-795 ◽  
Author(s):  
Honggang Jia ◽  
Yufeng Nie ◽  
Junlin Li
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Extended Finite Element Method ◽  
Intensity Factors ◽  
Extended Finite Element ◽  
Linear Elastic ◽  
Crack Problems ◽  
Good Accordance ◽  
Elastic Crack ◽  
Element Method

AbstractIn this paper, a method for extracting stress intensity factors (SIFs) in orthotropic thermoelasticity fracture by the extended finite element method (XFEM) and interaction integral method is present. The proposed method is utilized in linear elastic crack problems. The numerical results of the SIFs are presented and compared with those obtained using boundary element method (BEM). The good accordance among these two methods proves the applicability of the proposed approach and conforms its capability of efficiently extracting thermoelasticity fracture parameters in orthotropic material.

Stress Intensity Factor for Interfacial Cracks in Bi-Materials Using Incompatible Numerical Manifold Method

2011 ◽  
Vol 327 ◽  
pp. 109-114
Author(s):  
Gao Feng Wei ◽  
Hong Fen Gao ◽  
Hai Hui Jiang
Keyword(s):  
Stress Intensity ◽  
Interfacial Crack ◽  
Partition Of Unity ◽  
Complex Stress ◽  
Element Approximation ◽  
Numerical Manifold Method ◽  
Displacement Fields ◽  
Interfacial Cracks ◽  
Crack Problems ◽  
Numerical Manifold

Incompatible numerical manifold method (INMM) uses interpolation functions based on the concept of partition of unity, and considers the asymptotic solution and the discontinuity of displacement. This paper describes the application of INMM to bi-material interfacial crack. The two dimensional near-tip asymptotic displacement functions are added to the trial function approximation. This enables the domain to be modeled by manifold elements without explicitly meshing the crack surfaces. The crack-tip enrichment functions are chosen as those that span the asymptotic displacement fields for an interfacial crack. The INMM facilitates the incorporation of the oscillatory nature of the singularity within a conforming manifold element approximation. The complex stress intensity factors for bi-material interfacial cracks are numerically evaluated. Good agreement between the numerical results and the analytical solutions for benchmark interfacial crack problems is realized.

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