NUMERICAL ANALYSIS ON PROGRESSIVE FRACTURE BEHAVIOR BY USING ELEMENT-FREE METHOD BASED ON FINITE COVERS

2005 ◽  
Vol 02 (04) ◽  
pp. 543-553 ◽  
Author(s):  
MAOTIAN LUAN ◽  
XINHUI YANG ◽  
RONG TIAN ◽  
QING YANG
Keyword(s):  
Damage Model ◽  
Physical And Mechanical Properties ◽  
Least Square Method ◽  
Fracture Analysis ◽  
Least Square ◽  
Finite Cover ◽  
Moving Least Square ◽  
Progressive Fracture ◽  
Element Free Method ◽  
Element Free

The finite-cover element-free method FCEFM is applied to simulate the fracture and damage evolution process of geo-materials. This method is mathematically based on the finite-cover technique of manifold method and the multiple weighted moving least-square method to solve the continuous and discontinuous problems without meshing or re-meshing. The damage heterogeneity and evolutionary processes of rock mass with initial cracks are analyzed and numerically simulated by FCEFM. Using the method of probability to generate the parameters of materials randomly, the physical and mechanical properties of materials are randomly distributed in nodes or Gaussian points. And an alternating damage model together with numerical implementation which is adapted to microscopic elasto-brittle fracture analysis is proposed. Through analysis of several numerical examples, the validity and efficiency of progressive fracture analysis with use of the proposed FCEFM is demonstrated.

An adaptive orthogonal improved interpolating moving least-square method and a new boundary element-free method

2019 ◽  
Vol 353 ◽  
pp. 347-370 ◽  
Author(s):  
Qiao Wang ◽  
Wei Zhou ◽  
Y.T. Feng ◽  
Gang Ma ◽  
Yonggang Cheng ◽  
...  
Keyword(s):  
Boundary Element ◽  
Least Square Method ◽  
Least Square ◽  
Moving Least Square ◽  
Element Free Method ◽  
Element Free

An Efficient Meshfree Method for Fracture Analysis of Cracks in Bi-Materials

2006 ◽  
Author(s):  
B. Nandulal ◽  
B. N. Rao ◽  
C. Lakshmana Rao
Keyword(s):  
Computational Efficiency ◽  
Basis Function ◽  
Meshfree Method ◽  
Fracture Analysis ◽  
Least Square ◽  
Moving Least Square ◽  
Linear Elastic ◽  
Moving Least Square Approximation ◽  
Material Fracture ◽  
Element Free

This paper presents an enriched meshless method based on an improved moving least-square approximation (IMLS) method for fracture analysis of cracks in homogeneous, isotropic, linear-elastic, two-dimensional bimaterial solids, subject to mixed-mode loading conditions. The method involves an element-free Galerkin formulation in conjunction with IMLS and a new enriched basis functions to capture the singularity field in linear-elastic bi-material fracture mechanics. In the IMLS method, the orthogonal function system with a weight function is used as the basis function. The IMLS has higher computational efficiency and precision than the MLS, and will not lead to an ill-conditioned system of equations. The proposed enriched basis function can be viewed as a generalized enriched basis function, which degenerates to a linear-elastic basis function when the bimaterial constant is zero. Numerical examples are presented to illustrate the computational efficiency and accuracy of the proposed method.

scholarly journals The Interpolating Boundary Element-Free Method for Unilateral Problems Arising in Variational Inequalities

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Fen Li ◽  
Xiaolin Li
Keyword(s):  
Variational Inequalities ◽  
Boundary Element ◽  
Meshless Method ◽  
Boundary Integral Equations ◽  
Boundary Integral ◽  
Least Square ◽  
Moving Least Square ◽  
Unilateral Problems ◽  
Element Free Method ◽  
Element Free

The interpolating boundary element-free method (IBEFM) is developed in this paper for boundary-only analysis of unilateral problems which appear in variational inequalities. The IBEFM is a direct boundary only meshless method that combines an improved interpolating moving least-square scheme for constructing interpolation functions with boundary integral equations (BIEs) for representing governing equations. A projection operator is used to formulate the BIEs and then the formulae of the IBEFM are obtained for unilateral problems. The convergence of the developed meshless method is derived mathematically. The capability of the method is also illustrated and assessed through some numerical experiments.

The Element-Free Method for Steam Turbine Rotor

2013 ◽  
Vol 281 ◽  
pp. 343-346
Author(s):  
Su Ling Yuan
Keyword(s):  
Steam Turbine ◽  
Gaussian Quadrature ◽  
Turbine Rotor ◽  
Least Square ◽  
Gradient Field ◽  
Moving Least Square ◽  
Steam Turbine Rotor ◽  
Discrete Equations ◽  
Element Free Method ◽  
Element Free

The element-free method is a new numerical method, which requires only nodal data and whose shape functions are continual and differentiable. The element-free method employs moving least-square approximants to approximate original functions. In this paper, discrete equations of axial symmetry problem are obtained by variational principle and Gaussian quadrature. Several numerical examples indicate that the element-free method can obtain more accurate results about these problems, moreover, results and their gradients are continuous in the entire domain and post-processing to obtain a smooth gradient field is total unnecessary. Finaly, the element-free method is applied to heat conduction problems for steam turbine rotor.

Two dimensional element free Galerkin coupled flow function method and its application

2016 ◽  
Vol 33 (5) ◽  
pp. 1310-1326 ◽  
Author(s):  
Qingdong Zhang ◽  
Boyang Zhang ◽  
Xingfu Lu
Keyword(s):  
Function Method ◽  
Variational Equation ◽  
Least Square ◽  
Flow Function ◽  
Unknown Quantity ◽  
Content Type ◽  
Moving Least Square ◽  
Element Free Galerkin ◽  
Element Free Method ◽  
Element Free

Purpose – The purpose of this paper is to propose a hybridization numerical method to solve the plastic deformation of metal working based on the flow function method and meshless method. Design/methodology/approach – The proposed method is named as flow function-element free Galerkin (F-EFG) method. It uses the flow function as the basic unknown quantity to get the basic control equation, the compactly supported approximate function to establish a local approximate flow function by means of moving least square approximation, and the element free Galerkin (EFG) method to solve variational equation. The F-EFG method takes the upper limit method essence of flow function method, and the convergence, stability, and error characteristics of EFG method. Findings – The steady extrusion process of the axisymmetric extrusion problems as well as the extrusion deformation law and main field variables are subjects in the modeling and simulation analysis using F-EFG method. The results show that the F-EFG method has good computational efficiency and accuracy. Originality/value – The F-EFG method proposed in this paper has the advantages of high-solution precision of flow function method and large deformation solution of element free method. It overcomes the difficulties in global flow function establishment in flow function method and low-solution efficiency in element free method. The method is beneficial to the development of flow function method and element free method.

Analysis of element free Galerkin interloping moving least square method in an electrostatic problem

2015 ◽  
Vol 57 (6) ◽  
pp. 1390-1395 ◽  
Author(s):  
Úrsula C. Resende ◽  
Eduardo H. R. Coppoli ◽  
Marcio M. Afonso ◽  
Sandro T. M. Gonçalves
Keyword(s):  
Least Square Method ◽  
Least Square ◽  
Electrostatic Problem ◽  
Moving Least Square ◽  
Element Free Galerkin ◽  
Element Free

scholarly journals Superresolution of 3-D computational integral imaging based on moving least square method

2014 ◽  
Vol 22 (23) ◽  
pp. 28606 ◽  
Author(s):  
Hyein Kim ◽  
Sukho Lee ◽  
Taekyung Ryu ◽  
Jungho Yoon
Keyword(s):  
Least Square Method ◽  
Least Square ◽  
Integral Imaging ◽  
Moving Least Square ◽  
Computational Integral Imaging

USE OF B-SPLINE FUNCTION IN ELEMENT FREE GALERKIN METHOD FOR NUMERICAL SOLUTION OF PARTIAL DIFFERENTIAL EQUATION

2009 ◽  
Vol 06 (03) ◽  
pp. 349-360
Author(s):  
K. SANDEEP ◽  
K. KAMAL KUMAR
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Spline Function ◽  
Least Square ◽  
Partial Differential ◽  
Order Continuity ◽  
B Spline ◽  
Moving Least Square ◽  
Element Free Galerkin ◽  
Element Free

The paper presents application of a B-spline function in place of a shape function obtained by using moving least square approximant with B-spline weight and linear basis. The piecewise polynomial function of B-spline with C2 and lower order continuity is efficiently used in element free Galerkin (EFG) method to generate a new fast algorithm for the solution of one-dimensional partial differential equation. The support of B-spline function is assumed as the domain of influence of EFG method. The results of bar deflection are compared with those obtained by other researchers.

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