scholarly journals Finite-part integral and boundary element method to solve three-dimensional crack problems in piezoelectric materials

2007 ◽  
Vol 44 (14-15) ◽  
pp. 4770-4783 ◽  
Author(s):  
T.Y. Qin ◽  
Y.S. Yu ◽  
N.A. Noda
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Piezoelectric Materials ◽  
Three Dimensional ◽  
Finite Part ◽  
Crack Problems ◽  
Element Method

Dynamic Response of Three-Dimensional Multi-Domain Piezoelectric Structures via BEM

2018 ◽  
Vol 769 ◽  
pp. 317-322
Author(s):  
Leonid A. Igumnov ◽  
Ivan Markov ◽  
Aleksandr Lyubimov ◽  
Valery Novikov
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Piezoelectric Materials ◽  
Domain Boundary ◽  
Three Dimensional ◽  
Element Formulation ◽  
Laplace Domain ◽  
Piezoelectric Structures ◽  
Singular Representation ◽  
Element Method

In this paper, a Laplace domain boundary element method is applied for transient dynamic analysis of three-dimensional multi-domain linear piezoelectric structures. Piezoelectric materials of homogeneous sub-domains may have arbitrary degree of anisotropy. The boundary element formulation is based on a weakly singular representation of the piezoelectric boundary integral equations in the Laplace domain. To compute the time-domain solutions a convolution quadrature formula is applied for the numerical inversion of Laplace transform. Presented multi-domain boundary element method is tested on a three-dimensional problem of nonhomogeneous column which is made of two dissimilar piezoelectric materials and subjected to dynamic impact loading.

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.

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