scholarly journals A least square solution applied to plate analyses using the traction boundary integral equation

2012 ◽  
Author(s):  
L. Palermo
Keyword(s):  
Integral Equation ◽  
Boundary Integral Equation ◽  
Boundary Integral ◽  
Least Square

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.

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