On NGF Applications to LBIE Potential and Displacement Discontinuity Analyses

2010 ◽  
Vol 454 ◽  
pp. 127-135 ◽  
Author(s):  
L.S. Miers ◽  
J.C.F. Telles
Keyword(s):  
Integral Equation ◽  
Fracture Mechanics ◽  
Boundary Element ◽  
Boundary Integral Equation ◽  
Green's Function ◽  
Boundary Integral ◽  
Displacement Discontinuity ◽  
Local Boundary ◽  
Local Boundary Integral Equation ◽  
Companion Solution

This work aims at extending the concept of the Numerical Green's Function (NGF), known from boundary element applications to potential and fracture mechanics problems, to the Local Boundary Integral Equation (LBIE) context. As a "companion" solution, the NGF is used to remove the integrals of the main discontinuities over the crack boundary and is to be introduced only for source points whose support touches or contains the actual crack surfaces.

A Boundary Element Free Implementation Using NGF to Solve Fracture Mechanics Applications

2008 ◽  
Vol 383 ◽  
pp. 85-96 ◽  
Author(s):  
L.S. Miers ◽  
J.C.F. Telles
Keyword(s):  
Integral Equation ◽  
Fracture Mechanics ◽  
Boundary Element ◽  
Boundary Integral Equation ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Boundary Integral Equation Method ◽  
Equation Method ◽  
Local Boundary Integral Equation ◽  
Element Free

This work aims at introducing the concept of the numerical Green’s function (NGF) idea for elastostatic fracture mechanics using the boundary element-free method (BEFM). Unlike the local boundary integral equation method (LBIE), the BEFM only requires boundary interpolation. This method derives from the coupling of the boundary integral equation method and the orthogonal moving least-squares approximation scheme (OMLS). OMLS differs from standard MLS by using an orthogonal basis instead of only a linear independent one, which increases its accuracy and efficiency. Some illustrative examples are included in the end.

AN IMPROVED LOCAL BOUNDARY INTEGRAL EQUATION METHOD FOR TWO-DIMENSIONAL POTENTIAL PROBLEMS

2010 ◽  
Vol 02 (02) ◽  
pp. 421-436 ◽  
Author(s):  
BAODONG DAI ◽  
YUMIN CHENG
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Computational Efficiency ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Moving Least Squares ◽  
Two Dimensional ◽  
Local Boundary ◽  
Local Boundary Integral Equation ◽  
Potential Problems

Combining the local boundary integral equation with the improved moving least-squares (IMLS) approximation, an improved local boundary integral equation (ILBIE) method for two-dimensional potential problems is presented in this paper. In the IMLS approximation, the weighted orthogonal functions are used as basis functions. The IMLS approximation has greater computational efficiency and precision than the existing moving least-squares (MLS) approximation and does not lead to an ill-conditioned equations system. The corresponding formulae of the ILBIE method are obtained. Comparing with the conventional local boundary integral equation (LBIE) method, the ILBIE method is a direct meshless boundary integral equation method in which the basic unknown quantity is the real solution of the nodal variables, and the boundary conditions can be implemented directly and easily as in the finite element method. The ILBIE method has greater computational efficiency and precision. Some numerical examples to demonstrate the efficiency of the method are presented in this paper.

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