BIEM for 2D steady-state problems in cracked anisotropic materials

Dineva, Petia; Rangelov, Tsviatko; Groß, Dietmar

doi:10.1016/j.enganabound.2005.02.006

Cited by 24 publications

(9 citation statements)

References 35 publications

(65 reference statements)

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“…Here,

x \in Γ \cup {normalΓ}_{H}

;

c_{i j}

is the jump term depending on the local geometry at the collocation point

x (x_{1}, x_{2})

; the couple

x, ξ

presents the position vectors of the source and receiver, respectively;

U_{i j}^{*} false(x, ξ, ω false)

is the displacement fundamental solution of the governing elliptic partial differential Equation () for in‐plane wave motion in generally anisotropic solid, and its corresponding traction is

T_{i j}^{*} false(x, ξ, ω false) = C_{i j q l} U_{q k, l}^{*} false(x, ξ, ω false) n_{k}

, see Ref. [39], [40].…”

Section: Bvp Reformulation By Bies In Fourier Transform Domainmentioning

confidence: 99%

Transient response analysis of anisotropic solids with nano‐cavities by BEM

Parvanova

Dineva

2020

Z Angew Math Mech

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Тwo‐dimensional in‐plane transient elasto‐dynamic problem for isotropic/anisotropic, finite/infinite solids with nano‐cavities is formulated. The mechanical model combines: (a) classical elastodynamic theory for the bulk anisotropic solid; (b) non‐classical boundary conditions and localized constitutive equation for the interface between nano‐cavities and anisotropic matrix within the frame of the Gurtin‐Murdoch surface elasticity theory. The computational approach uses Fourier‐domain BEM (boundary element method) in conjunction with closed form frequency dependent fundamental solution. Accuracy and convergence of the numerical solutions for dynamic stress concentration factor (DSCF) and scattered wave field displacements is studied by comparison with available solutions. In addition a parametric study for the transient wave field sensitivity in bounded and unbounded solids to the type and characteristics of the transient disturbance, to the surface elasticity phenomena, to the nano‐cavities interaction and to the type of the material anisotropy is presented.

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“…Here,

x \in Γ \cup {normalΓ}_{H}

;

c_{i j}

is the jump term depending on the local geometry at the collocation point

x (x_{1}, x_{2})

; the couple

x, ξ

presents the position vectors of the source and receiver, respectively;

U_{i j}^{*} false(x, ξ, ω false)

is the displacement fundamental solution of the governing elliptic partial differential Equation () for in‐plane wave motion in generally anisotropic solid, and its corresponding traction is

T_{i j}^{*} false(x, ξ, ω false) = C_{i j q l} U_{q k, l}^{*} false(x, ξ, ω false) n_{k}

, see Ref. [39], [40].…”

Section: Bvp Reformulation By Bies In Fourier Transform Domainmentioning

confidence: 99%

Transient response analysis of anisotropic solids with nano‐cavities by BEM

Parvanova

Dineva

2020

Z Angew Math Mech

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“…Boundary integral equation method has been applied by Dineva et al (2002Dineva et al ( , 2005. Transient elastodynamic crack analysis in twodimensional, layered, anisotropic and linear elastic solids has been addressed by Wunsche et al (2009) using the boundary element method (BEM) in conjunction with a multi-domain technique.…”

Section: Introductionmentioning

confidence: 99%

Dynamic response of interfacial finite cracks in orthotropic materials subjected to concentrated loads

Rubio-González

Lira-Vergara

2011

Int J Fract

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The elastodynamic response of an infinite non-homogeneous orthotropic material with an interfacial finite crack under concentrated normal and shear impact loads is examined. Solution for the stress intensity factor history around the crack tips is found. Laplace and Fourier transforms are employed to solve the equations of motion leading to a Fredholm integral equation on the Laplace transform domain. The dynamic stress intensity factor history can be computed by numerical Laplace transform inversion of the solution of the Fredholm equation. Numerical values of the dynamic stress intensity factor history for some materials are obtained. Interfacial cracks between two different materials and between two pieces of the same material but different fiber orientation are considered. This solution can be used as a Green's function to solve dynamic problems involving interfacial finite cracks in orthotropic bimaterials.

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“…Three different BEM formulations, namely, the frequency domain [8,9,18,40] the Laplace transform domain [13] and the time domain BEM [12,15,19,29 31,35,36,41 43] are often applied to the elastodynamic crack analysis. Comparative study of the different BEM formulations and analysis of their accuracy and efficiency, is performed in [16,34] for elastodynamic problems without considering possibilities for contact integration.…”

Section: Introductionmentioning

confidence: 99%

Comparative study of time and frequency domain BEM approaches in frictional contact problem for antiplane crack under harmonic loading

Zozulya

2013

Engineering Analysis with Boundary Elements

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International audienceTwo different boundary element methods (BEM) for crack analysis in two dimensional (2 D) antiplane, homogeneous, isotropic and linear elastic solids by considering frictional contact of the crack edges are presented. Hypersingular boundary integral equations (BIE) in time domain (TD) and frequency domain (FD), with corresponding elastodynamic fundamental solutions are applied for this purpose. For evaluation of the hypersingular integrals involved in BIEs a special regularization process that converts the hypersingular integrals to regular integrals is applied. Simple regular formulas for their calculation are presented. For the problems solution while considering frictional contact of the crack edges a special iterative algorithm of Udzava's type is elaborated and used. Numerical results for crack opening, frictional contact forces and dynamic stress intensity factors (SIFs) are presented and discussed for a finite III mode crack in an infinite domain subjected to a harmonic crack face loading and considering crack edges frictional contact interaction using the TD and FD approaches

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BIEM for 2D steady-state problems in cracked anisotropic materials

Cited by 24 publications

References 35 publications

Transient response analysis of anisotropic solids with nano‐cavities by BEM

Transient response analysis of anisotropic solids with nano‐cavities by BEM

Dynamic response of interfacial finite cracks in orthotropic materials subjected to concentrated loads

Comparative study of time and frequency domain BEM approaches in frictional contact problem for antiplane crack under harmonic loading

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