Multidomain boundary integral formulation for piezoelectric materials fracture mechanics

Davi, Giuseppe; Milazzo, Alberto

doi:10.1016/s0020-7683(00)00416-9

Cited by 67 publications

(24 citation statements)

References 31 publications

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“…In terms of modelling and solving for piezoelectric applications with BEM, much research has been devoted to investigating the behaviour of piezoelectric material itself [17,18]. For modelling piezoelectric smart structures in SHM, Leme et al [19] established a static model for the analysis of 2D plates bonded with piezoelectric sensors which are formulated as beams.…”

Section: Introductionmentioning

confidence: 99%

A boundary element model for structural health monitoring using piezoelectric transducers

Zou

Benedetti

Aliabadi

2013

Smart Mater. Struct.

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In this paper, for the first time, the boundary element method (BEM) is used for modelling smart structures instrumented with piezoelectric actuators and sensors. The host structure and its cracks are formulated with the 3D dual boundary element method (DBEM), and the modelling of the piezoelectric transducers implements a 3D semi-analytical finite element approach. The elastodynamic analysis of the structure is performed in the Laplace domain and the time history is obtained by inverse Laplace transform. The sensor signals obtained from BEM simulations show excellent agreement with those from FEM simulations and experiments. This work provides an alternative methodology for modelling smart structures in structural health monitoring (SHM) applications.

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Section: Introductionmentioning

confidence: 99%

A boundary element model for structural health monitoring using piezoelectric transducers

Zou

Benedetti

Aliabadi

2013

Smart Mater. Struct.

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“…where U = u 1 u 2 u 3 u ½ T is the generalized displacement vector, collecting the mechanical displacements u i and the electric potential u, R is the generalized stiffness matrix, and D D the generalized differential operator (Davı`and Milazzo, 2001), explicitly defined for completeness in the Appendix. Assuming quasi-static electric field, the right-hand side of Equation (1) represents only the inertial force components, and the inertia matrix r assumes the following form:…”

Section: Boundary Integral (Bi) Representation and Fundamental Solutionsmentioning

confidence: 99%

“…The expression of the fundamental solutions can be found in the study by Davı`and Milazzo (2001). The domain integral in the right-hand side of Equation ( 3) represents the inertial term that contains the unknown acceleration € U(P) inside the domain.…”

Section: Boundary Integral (Bi) Representation and Fundamental Solutionsmentioning

confidence: 99%

On the dynamic behavior of piezoelectric active repair by the boundary element method

Alaimo

Milazzo

Orlando

2011

Journal of Intelligent Material Systems and Structures

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The dynamic behavior of piezoelectric active repair bonded on cracked structures is analyzed in this article. The boundary\ud element code used to perform the simulations is implemented in the framework of piezoelectricity in order to\ud model the coupling between the elastic and the electric fields, which represents the most important feature of piezoelectric\ud media. The fracture mechanics problem, i.e. the crack, as well as the bonding layer between the host structure and\ud the active patch is modeled by means of the multidomain technique provided with an interface spring model. More particularly,\ud the spring interface model allows considering the bonding layer as a zero-thickness elastic ply characterized by\ud normal and tangential stiffness constants. The crack is also modeled as an elastic interface characterized by vanishing\ud stiffness. The dual reciprocity method (DRM) has been used in the present time-dependent application for the approximation\ud of the domain inertia terms. Numerical analyses have been carried out in order to characterize the dynamic\ud repairing mechanism of the assembled structure by means of the computation of the dynamic stress intensity factors\ud and discussions are presented to highlight the effect of the inertial forces on the fracture mechanics behavior of the overall\ud assembled structure

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“…One of the earliest approaches was the use of specific Green's functions that intrinsically account for the presence of the crack in the domain and avoid the discretisation the crack itself [6,7,8]; however such a technique is based on the knowledge of different Green's functions for different crack geometries, which in many cases are difficult, if not impossible, to evaluate. Another powerful and versatile approach for modelling cracked domains using the BEM is the multi-region technique, which is based on a subdivision of the domain into subregions whose boundaries contain the crack [9,10,11]. Then, to retrieve the behaviour of the original domain, continuity/equilibrium interface conditions are enforced on the newly introduced boundaries, whereas traction-free boundary conditions are enforced over the crack surfaces.…”

Section: Introductionmentioning

confidence: 99%

A novel boundary element formulation for anisotropic fracture mechanics

Gulizzi

Benedetti

Milazzo

2019

Theoretical and Applied Fracture Mechanics

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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 then obtained using such representation into the integral expression of the aforementioned Laplace equation and employing the relationship between the stress function gradient and the boundary tractions. The supplementary equation neither requires the computation of hyper-singular integrals nor does it introduce additional variables for the problem, as it involves boundary displacements and tractions only. Numerical results are obtained for both uncracked and cracked bodies and show the accuracy and potential of the proposed approach.

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Multidomain boundary integral formulation for piezoelectric materials fracture mechanics

Cited by 67 publications

References 31 publications

A boundary element model for structural health monitoring using piezoelectric transducers

A boundary element model for structural health monitoring using piezoelectric transducers

On the dynamic behavior of piezoelectric active repair by the boundary element method

A novel boundary element formulation for anisotropic fracture mechanics

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