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.

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.

The Element-Free Galerkin Method for the Unsteady Magnetohydrodynamic Flow in a Duct

2015 ◽  
Vol 723 ◽  
pp. 181-185
Author(s):  
Xing Hui Cai ◽  
Hong Fu Qiang ◽  
Jiang Ren Lu ◽  
Guo Liang Wang
Keyword(s):  
Galerkin Method ◽  
Numerical Solutions ◽  
Magnetohydrodynamic Flow ◽  
Least Square ◽  
Element Free Galerkin Method ◽  
Moving Least Square ◽  
Coupled Equations ◽  
Element Free Galerkin ◽  
Moving Least Square Approximation ◽  
Element Free

In this paper, a meshless global element-free Galerkin method is given to obtain the numerical solutions of the coupled equations in the velocity and magnetic field for the unsteady magnetohydrodynamic flow through a straight duct with arbitrary electrical conductivity, that is, from perfectly conducting to insulated duct walls. The moving least-square approximation scheme is employed to construct shape functions. A time stepping method is employed to deal with the time derivatives. Non-uniform background grids and nodes are applied for numerical simulations. Computations are performed for different Hartmann numbers and wall conductivities at different time.

A modified method to determine the radius of influence domain in element-free Galerkin method

2014 ◽  
Vol 229 (5) ◽  
pp. 795-805 ◽  
Author(s):  
Mao Sheng ◽  
Gensheng Li ◽  
Subhash Shah
Keyword(s):  
Least Square ◽  
Patch Tests ◽  
Moving Least Square ◽  
Modified Method ◽  
Point Of Interest ◽  
Element Free Galerkin ◽  
Radius Of Influence ◽  
Moving Least Square Approximation ◽  
Random Node ◽  
Element Free

The radius of the influence domain is an important parameter in the weight function and plays an essential role in the accuracy of approximations. A modified method was proposed for determining the radius of influence domain. The modification is that the radius of influence domain is prescribed by the desired amount of support nodes for any point of interest. The advantages of this strategy are the regularity of matrix can be ensured in moving least square approximation and the algorithm is simple and practicable. The modified method was validated by thousands of patch tests in the case of regular and irregular node collocations and Timoshenko beam problem with using random node collocation. Results show that the proposed method performs more capability to handle the arbitrary node collocation than the pre-existing methods. This paper provides an alternative way to determine the radius of influence domain.

A New Meshless Simulated Method of Chloride Diffusion in Concrete

2014 ◽  
Vol 1051 ◽  
pp. 725-729
Author(s):  
Ling Yao ◽  
Ling Zhang ◽  
Ling Ling Zhang ◽  
Xin Yue Zhang ◽  
Yong Jing Wang
Keyword(s):  
Chloride Content ◽  
Chloride Ions ◽  
Least Square ◽  
Chloride Diffusion ◽  
Element Free Galerkin Method ◽  
Error Norm ◽  
Moving Least Square ◽  
Element Free Galerkin ◽  
Moving Least Square Approximation ◽  
Element Free

In this paper, θ-EFG(theθfamily of methods –Element Free Galerkin) method is developed and adopted for the simulation of chloride diffusion in concrete. Diffusion of chloride ions is generally assumed to follow the Fick’s second law and its solving process usually adopts finite element and finite difference method. θ-EFG is a meshless method which uses a moving least square approximation in space domain, then uses the θ family of methods in time domain. Some discussions and One dimensional examples are carried out. The computational results compared with the analytical solution are shown that the relative error norm that time=20years, chloride content of different depth and depth =45 mm, chloride content are about 0.5% and 1% respectively.

Wrinkling Analysis of Pre-Stressed Rectangular Membranes Using Element-Free Galerkin Method

2020 ◽  
pp. 2041001
Author(s):  
K. R. Unnikrishnan ◽  
I. R. Praveen Krishna ◽  
C. O. Arun
Keyword(s):  
Galerkin Method ◽  
Degrees Of Freedom ◽  
Least Square ◽  
Element Free Galerkin Method ◽  
Moving Least Square ◽  
Element Free Galerkin ◽  
Wrinkling Analysis ◽  
Moving Least Square Approximation ◽  
Element Free ◽  
The Mathematical Model

In this study, element-free Galerkin method (EFGM), a meshless method, is proposed for wrinkling analysis of pre-stressed rectangular membranes. The mathematical model for studying wrinkling of pre-stressed membranes is derived by considering the bending stiffness, though it is negligible. Moving least-square approximation for deflection is constructed by considering three degrees of freedom per node. Essential boundary conditions are imposed using scaled transformation matrix method. Initially, compression-induced buckling of a homogeneous thin plate without pre-stress is solved to validate the method and then a pre-stressed homogeneous membrane is analyzed for both compression-induced and shear-induced wrinkling. Capabilities of the proposed method for membrane analysis are compared with that of the finite element method (FEM). Comparative study on wrinkling analysis using EFGM and different FEM element types in a commercial FEM package shows that in lower modes both methods show satisfying consistency in eigenvalues with respect to the total of number of nodes, while at higher modes EFGM shows better consistency than FEM. Further, the study is extended to wrinkling of nonhomogeneous membranes subjected to linearly-varying in-plane load. The results obtained from EFGM analysis is compared and found to be matching well with those available in the literature.

scholarly journals A New and Efficient Boundary Element-Free Method for 2-D Crack Problems

2017 ◽  
Vol 2017 ◽  
pp. 1-9
Author(s):  
Jinchao Yue ◽  
Liwu Chang ◽  
Yuzhou Sun
Keyword(s):  
Integral Equation ◽  
Boundary Element ◽  
Boundary Integral Equation ◽  
Boundary Integral ◽  
Least Square ◽  
Moving Least Square ◽  
Crack Problems ◽  
Moving Least Square Approximation ◽  
New Variables ◽  
Element Free

An efficient boundary element-free method is established for 2-D crack problems by combining a pair of boundary integral equations and the moving-least square approximation. The displacement boundary integral equation is collated on the on-crack boundary, and a new traction boundary integral equation is applied on the crack surface without the separate consideration of the upper and lower sides. In virtue of integration by parts, only singularity in order 1/r is involved in the integral kernels of new traction boundary integral equation, which brings convenience to the numerical implementation. Meanwhile, the integration by parts produces the new variables, the displacement density, and displacement dislocation density, and they are the coexisting unknowns along with the displacement and displacement dislocation. With the high-order continuity of the moving-least square approximation, these new variables are directly approximated with the nodal displacement or displacement dislocation, and the final system of equations contains the unknowns of nodal displacements and displacement dislocations only. The boundary element-free computational scheme is established, and several examples show the efficiency and flexibility of the proposed method.

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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