A numerical integration strategy of meshless numerical manifold method based on physical cover and applications to linear elastic fractures

2022 ◽  
Vol 134 ◽  
pp. 79-95
Author(s):  
Wei Li ◽  
Xianbin Yu ◽  
Shan Lin ◽  
Xin Qu ◽  
Xizhen Sun
Keyword(s):  
Numerical Integration ◽  
Numerical Manifold Method ◽  
Linear Elastic ◽  
Integration Strategy ◽  
Numerical Manifold

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.

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.

New Numerical Quadrature of Integrand with Singularity of 1/r and its Application

2013 ◽  
Vol 444-445 ◽  
pp. 641-649
Author(s):  
Dong Dong Xu ◽  
Hong Zheng ◽  
Kai Wen Xia
Keyword(s):  
Numerical Integration ◽  
Stiffness Matrix ◽  
Numerical Manifold Method ◽  
Reference Solution ◽  
Quadrature Method ◽  
Linear Fracture ◽  
Elastic Fracture ◽  
Numerical Manifold ◽  
Duffy Transformation ◽  
Good Agreement

A new quadrature method is proposed for numerical integration of integrands with the singularity of 1/r occurring at the computation of stiffness matrix when a singular physical cover is introduced to the numerical manifold method (NMM) for linear fracture problems. The detailed proof is presented, which shows the Jacobian has a factor of r that can be used to eliminate the singularity. Compared with the Duffy transformation, it proves more simple and easier to implement while owning the same precision. A numerical example in elastic fracture by the NMM is presented to illustrate the performance of the proposed method. The result has a good agreement with the reference solution.

scholarly journals Numerical Manifold Method with Endochronic Theory for Elastoplasticity Analysis

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Wei Zeng ◽  
Junjie Li ◽  
Fei Kang
Keyword(s):  
Soft Clay ◽  
Crack Problem ◽  
Numerical Manifold Method ◽  
Traffic Loading ◽  
Endochronic Theory ◽  
Linear Elastic ◽  
Numerical Tests ◽  
Loading Problem ◽  
Numerical Manifold ◽  
Discontinuous Problems

Numerical manifold method (NMM) was originally developed based on linear elastic constitutive model. For many problems it is difficult to obtain accurate results without elastoplasticity analysis, and an elastoplasticity version of NMM is needed. In this paper, the incremental endochronic theory is extended into NMM analysis and an endochronic NMM algorithm is proposed for elastoplasticity analysis. It is well known that endochronic theory is one of the widely used elastoplasticity theories which can deal with elastoplasticity problems without a yield surface and loading or unloading judgments. Numerical tests show that the proposed algorithm of endochronic NMM possesses a good accuracy. The proposed algorithm is also applied to analyze a crack problem and a soft clay foundation under traffic loading problem. Results demonstrate the convenience of the endochronic NMM in analyzing elastoplasticity discontinuous problems.

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 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
Sign in / Sign up

Export Citation Format

Share Document