Search results for "dual boundary element method"
showing 8 items of 8 documents
Alternative boundary integral equations for fracture mechanics in 2D anisotropic bodies
2017
An alternative dual boundary element formulation for generally anisotropic linear elastic twodimensional bodies is presented in this contribution. The formulation is based on the decomposition of the displacement field into the sum of a vector field satisfying the anisotropic Laplace equation and the gradient of the classic Airy stress function. By suitable manipulation of the integral representation of the anisotropic Laplace equation, a set of alternative integral equations is obtained, which can be used in combination with the displacement boundary integral equation for the solution of crack problems. Such boundary integral equations have the advantage of avoiding hyper-singular integral…
Dual Boundary Element Method for fatigue crack growth: implementation of the Richard’s criterion
2013
A new criterion for fatigue crack growth, whose accuracy was previously tested in the literature with the Finite Element Method, is here adopted with a Dual Boundary Element formulation. The fatigue crack growth of an elliptical inclined crack, embedded in a three dimensional cylindrical bar, is analyzed. In this way in addition to the propagation angle estimated by the Sih’s criterion, it is possible to take into account a twist propagation angle. The two propagation criteria are compared in terms of shape of the propagated crack and in terms of SIFs along the crack front. The efficiency of the Dual Boundary Element Method in this study is highlighted.
A fast dual boundary element method for 3D anisotropic crack problems
2009
In the present paper a fast solver for dual boundary element analysis of 3D anisotropic crack problems is formulated, implemented and tested. The fast solver is based on the use of hierarchical matrices for the representation of the collocation matrix. The admissible low rank blocks are computed by adaptive cross approximation (ACA). The performance of ACA against the accuracy of the adopted computational scheme for the evaluation of the anisotropic kernels is investigated, focusing on the balance between the kernel representation accuracy and the accuracy required for ACA. The system solution is computed by a preconditioned GMRES and the preconditioner is built exploiting the hierarchical …
A fast hierarchical dual boundary element method for three-dimensional elastodynamic crack problems
2010
In this work a fast solver for large-scale three-dimensional elastodynamic crack problems is presented, implemented, and tested. The dual boundary element method in the Laplace transform domain is used for the accurate dynamic analysis of cracked bodies. The fast solution procedure is based on the use of hierarchical matrices for the representation of the collocation matrix for each computed value of the Laplace parameter. An ACA (adaptive cross approximation) algorithm is used for the population of the low rank blocks and its performance at varying Laplace parameters is investigated. A preconditioned GMRES is used for the solution of the resulting algebraic system of equations. The precond…
Structures with Surface-Bonded PZT Piezoelectric Patches: a BEM Investigation into the Strain-transfer Mechanism for SHM applications
2009
In this work a three-dimensional BEM model is used for the analysis of structures with cracks and surface bonded piezoelectric PZT patches used as strain sensors. The cracked structure is modelled by the dual boundary element method, which allows for accurate and reliable crack analysis, while the piezoelectric patch is analyzed by a finite element state-space approach, that embodies both the full electro-mechanical coupling and the suitable sensor’s boundary conditions. The model is used to investigate the strain-transfer mechanism from an host elastic structure to the piezoelectric layer, taking into account the effect of the adhesive layer, as well as the mechanical interaction between t…
A novel boundary element formulation for anisotropic fracture mechanics
2019
Abstract A novel boundary element formulation for two-dimensional fracture mechanics is presented in this work. The formulation is based on the derivation of a supplementary boundary integral equation to be used in combination with the classic displacement boundary integral equation to solve anisotropic fracture mechanics problems via a single-region approach. The formulation is built starting from the observation that the displacement field for an anisotropic domain can be represented as the superposition of a vector field, whose components satisfy a suitably defined anisotropic Laplace equation, and the gradient of the Airy stress function. The supplementary boundary integral equation is …
A fast 3D dual boundary element method based on hierarchical matrices
2008
AbstractIn this paper a fast solver for three-dimensional BEM and DBEM is developed. The technique is based on the use of hierarchical matrices for the representation of the collocation matrix and uses a preconditioned GMRES for the solution of the algebraic system of equations. The preconditioner is built exploiting the hierarchical arithmetic and taking full advantage of the hierarchical format. Special algorithms are developed to deal with crack problems within the context of DBEM. The structure of DBEM matrices has been efficiently exploited and it has been demonstrated that, since the cracks form only small parts of the whole structure, the use of hierarchical matrices can be particula…
Dual boundary element model of 3D piezoelectric smart structures
2017
In this paper, the application of the dual boundary element method (DBEM) in the field of structural health monitoring (SHM) is explored. The model involves a 3D host structure, which is formulated by the DBEM in the Laplace domain, and 3D piezoelectric transducers, whose finite element model is derived from the electro-mechanical behaviour of piezoelectricity. The piezoelectric transducers and the host structure are coupled together via BEM variables. The practicability of this method in active sensing applications is demonstrated through comparisons with established FEM and parametric studies.