Symmetric Galerkin boundary integral fracture analysis for plane orthotropic elasticity

1997 ◽  
Vol 20 (1-2) ◽  
pp. 26-33 ◽  
Author(s):  
L. J. Gray ◽  
G. H. Paulino
Keyword(s):  
Fracture Analysis ◽  
Boundary Integral ◽  
Orthotropic Elasticity

Dynamic Fracture Analysis of Plates Loaded in Tension and Bending Using the Dual Boundary Element Method

2019 ◽  
Vol 827 ◽  
pp. 440-445
Author(s):  
Jun Li ◽  
Zahra Sharif Khodaei ◽  
Ferri M.H. Aliabadi
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Dynamic Fracture ◽  
Boundary Integral Equations ◽  
Crack Opening ◽  
Fracture Analysis ◽  
Boundary Integral ◽  
Mindlin Plate ◽  
Dual Boundary Element Method ◽  
Element Method

The purpose of this paper is to solve dynamic fracture problems of plates under both tension and bending using the boundary element method (BEM). The dynamic problems were solved in the Laplace-transform domain, which avoided the calculation of the domain integrals resulting from the inertial terms. The dual boundary element method, in which both displacement and traction boundary integral equations are utilized, was applied to the modelling of cracks. The dynamic fracture analysis of a plate under combined tension and bending loads was conducted using the BEM formulations for the generalized plane stress theory and Mindlin plate bending theory. Dynamic stress intensity factors were estimated based on the crack opening displacements.

A Boundary Element-Free Method for Fracture Analysis of 2D Anisotropic Solids

2010 ◽  
Vol 139-141 ◽  
pp. 107-112
Author(s):  
Yu Zhou Sun ◽  
Dong Xia Li ◽  
Hui Wang
Keyword(s):  
Dislocation Density ◽  
Weight Function ◽  
Boundary Element ◽  
Fracture Analysis ◽  
Boundary Integral ◽  
Computational Method ◽  
Element Free Method ◽  
Mls Approximation ◽  
New Variables ◽  
Element Free

This paper presents a boundary element-free computational method for the fracture analysis of 2-D anisotropic bodies. The study starts from a derived traction boundary integral equation (BIE) in which the boundary conditions of both upper and lower crack surfaces are incorporated into and only the Cauchy singular kernal is involved. The boundary element-free method is achieved by combining this new BIE and the moving least-squares (MLS) approximation. The new BIE introduces two new variables: the displace density and The dislocation density. For each crack, the dislocation density is first expressed as the product of the characteristic term and unknown weight function, and the unknown weight function is approximated with the MLS approximation. The stress intensity factors (SIFs) can be calculated from the the weight function. The examples of the straight and circular-arc cracks are computed, and the convergence and efficiency are discussed.

scholarly journals Hypersingular boundary integral equations for plane orthotropic elasticity in terms of first-order stress functions

2020 ◽  
Vol 15 (2) ◽  
pp. 185-207
Author(s):  
Sándor Szirbik
Keyword(s):  
Stress Distribution ◽  
Integral Equations ◽  
Boundary Integral Equations ◽  
Arbitrary Point ◽  
Boundary Integral ◽  
Computational Technique ◽  
First Order ◽  
Orthotropic Elasticity ◽  
Stress Functions ◽  
Order Stress

This paper is intended to present an implementation of the hypersingular boundary integral equations in terms of first-order stress functions for stress computations in plane orthotropic elasticity. In general, the traditional computational technique of the boundary element method used for computing the stress distribution on the boundary and close to it is not as accurate as it should be. In contrast, the accuracy of stress computations on the boundary is greatly increased by applying the hypersingular integral equations. Contrary to the method in which the solution is based on an approximation of displacement field, here the first-order stress functions and the rigid body rotation are the fundamental variables. An advantage of this approach is that the stress components can be obtained directly from the stress functions, there is, therefore, no need for Hooke's law, which should be used when they are computed from displacements. In addition, the computational work can be reduced when the stress distribution is computed at an arbitrary point on the boundary. The numerical examples presented prove the efficiency of this technique.

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