scholarly journals An isogeometric SGBEM for crack problems of magneto-electro-elastic materials

2017 ◽  
Vol 39 (2) ◽  
pp. 135-147 ◽  
Author(s):  
Han Duc Tran ◽  
Binh Huy Nguyen
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Basis Functions ◽  
Intensity Factors ◽  
B Splines ◽  
Crack Problems ◽  
Generalized Stress Intensity Factors ◽  
Galerkin Boundary Element Method ◽  
Finite Domains ◽  
Element Method

The isogeometric symmetric Galerkin boundary element method is applied for the analysis of crack problems in two-dimensional magneto-electro-elastic domains. In this method, the field variables of the governing integral equations as well as the geometry of the problems are approximated using non-uniform rational B-splines (NURBS) basis functions. The key advantage of this method is that the isogeometric analysis and boundary element method deal only with the boundary of the domain. To verify the accuracy of the proposed method, numerical examples for crack problems in infinite and finite domains are examined. It is observed that the computed generalized stress intensity factors obtained by the proposed method agree well with the exact solutions and other references.

A Simple Galerkin Boundary Element Method for Three-Dimensional Crack Problems in Functionally Graded Materials

2005 ◽  
Vol 492-493 ◽  
pp. 367-372
Author(s):  
Glaucio H. Paulino ◽  
Alok Sutradhar
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Functionally Graded Materials ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Graded Materials ◽  
Simple Boundary ◽  
Crack Problems ◽  
Galerkin Boundary Element Method ◽  
Element Method

This paper presents a Galerkin boundary element method for solving crack problems governed by potential theory in nonhomogeneous media. In the simple boundary element method, the nonhomogeneous problem is reduced to a homogeneous problem using variable transformation. Cracks in heat conduction problem in functionally graded materials are investigated. The thermal conductivity varies parabolically in one or more coordinates. A three dimensional boundary element implementation using the Galerkin approach is presented. A numerical example demonstrates the eáciency of the method. The result of the test example is in agreement with ßnite element simulation results.

An Effective Numerical Approach for Multiple Void-Crack Interaction

2005 ◽  
Vol 73 (4) ◽  
pp. 525-535 ◽  
Author(s):  
Xiangqiao Yan
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Elastic Plate ◽  
Homogeneous Problem ◽  
Crack Problem ◽  
General System ◽  
Numerical Approach ◽  
Displacement Discontinuity ◽  
Crack Problems ◽  
Element Method

This paper presents a numerical approach to modeling a general system containing multiple interacting cracks and voids in an infinite elastic plate under remote uniform stresses. By extending Bueckner’s principle suited for a crack to a general system containing multiple interacting cracks and voids, the original problem is divided into a homogeneous problem (the one without cracks and voids) subjected to remote loads and a multiple void-crack problem in an unloaded body with applied tractions on the surfaces of cracks and voids. Thus the results in terms of the stress intensity factors (SIFs) can be obtained by considering the latter problem, which is analyzed easily by means of the displacement discontinuity method with crack-tip elements (a boundary element method) proposed recently by the author. Test examples are included to illustrate that the numerical approach is very simple and effective for analyzing multiple crack/void problems in an infinite elastic plate. Specifically, the numerical approach is used to study the microdefect-finite main crack linear elastic interaction. In addition, complex crack problems in infinite/finite plate are examined to test further the accuracy and robustness of the boundary element method.

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