scholarly journals Dynamic interaction of cracks in piezoelectric and anisotropic solids: A non-hypersingular BIEM approach

2008 ◽  
Vol 35 (1-3) ◽  
pp. 73-91 ◽  
Author(s):  
Petia Dineva ◽  
Dietmar Gross ◽  
Tsviatko Rangelov
Keyword(s):  
Electromechanical Coupling ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Crack Interaction ◽  
Wave Loading ◽  
Intensity Factors ◽  
Frequency Dependent ◽  
Time Harmonic ◽  
Arbitrary Position ◽  
Complex Influence

A non-hypersingular traction boundary integral equation method (BIEM) is proposed for the treatment of crack systems in piezoelectric or anisotropic plane domains loaded by time-harmonic waves. The solution is based on the frequency dependent fundamental solution obtained by Radon transform. The proposed method is flexible, numerically efficient and has virtually no limitations regarding the material type, crack geometry and type of wave loading. The accuracy and convergence of the BIEM solution for stress intensity factors is validated by comparison with existing results from the literature. Simulations for different crack configurations such as coplanar collinear or cracks in arbitrary position to each other are presented and discussed. They demonstrate among others the strong effect of electromechanical coupling, show the frequency dependent shielding and amplification resulting from crack interaction and reveal the sensitivity of the K-factors on the complex influence of both wave-crack and crack-crack interaction.

The inverse elastic scattering by an impenetrable obstacle and a crack

2020 ◽  
Author(s):  
Jianli Xiang ◽  
Guozheng Yan
Keyword(s):  
Mixed Type ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Field Operator ◽  
Integral Equation Method ◽  
Factorization Method ◽  
Boundary Integral ◽  
Far Field ◽  
Direct Scattering ◽  
Time Harmonic

Abstract This paper is concerned with the inverse scattering problem of time-harmonic elastic waves by a mixed-type scatterer, which is given as the union of an impenetrable obstacle and a crack. We develop the modified factorization method to determine the shape of the mixed-type scatterer from the far field data. However, the factorization of the far field operator $F$ is related to the boundary integral matrix operator $A$, which is obtained in the study of the direct scattering problem. So, in the first part, we show the well posedness of the direct scattering problem by the boundary integral equation method. Some numerical examples are presented at the end of the paper to demonstrate the feasibility and effectiveness of the inverse algorithm.

A New Boundary Integral Equation Method for Cracked Piezoelectric Bodies

2006 ◽  
Vol 306-308 ◽  
pp. 465-470 ◽  
Author(s):  
Kuang-Chong Wu
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Present Method ◽  
Boundary Integral Equations ◽  
Integral Formula ◽  
Electric Displacement ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Equation Method ◽  
Intensity Factors

A novel integral equation method is developed in this paper for the analysis of two-dimensional general piezoelectric cracked bodies. In contrast to the conventional boundary integral methods based on reciprocal work theorem, the present method is derived from Stroh’s formalism for anisotropic elasticity in conjunction with Cauchy’s integral formula. The proposed boundary integral equations contain generalized boundary displacement (displacements and electric potential) gradients and generalized tractions (tractions and electric displacement) on the non-crack boundary, and the generalized dislocations on the crack lines. The boundary integral equations can be solved using Gaussian-type integration formulas without dividing the boundary into discrete elements. The crack-tip singularity is explicitly incorporated and the generalized intensity factors can be computed directly. Numerical examples of generalized stress intensity factors are given to illustrate the effectiveness and accuracy of the present method.

scholarly journals A Source Problem for the Helmholtz Equation via a Dirichlet-to-Neumann Map

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Kuo-Ming Lee
Keyword(s):  
Integral Equation ◽  
Helmholtz Equation ◽  
Dimensional Space ◽  
Integral Operators ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Two Dimensional ◽  
Time Harmonic ◽  
Boundary Integral Operators ◽  
Dirichlet To Neumann Map

In this paper, we consider a source problem for a time harmonic acoustic wave in two-dimensional space. Based on the boundary integral equation method, a Dirichlet-to-Neumann map in terms of boundary integral operators on the boundary of the source is constructed to transform this problem into two boundary value problems for the Helmholtz equation.

Micromechanical Dynamic Influence of Rigid Disk-Shaped Inclusion on Neighboring Crack in 3D Elastic Matrix

2007 ◽  
Vol 567-568 ◽  
pp. 133-136 ◽  
Author(s):  
Victor V. Mykhas'kiv ◽  
O. Khay ◽  
Jan Sladek ◽  
Vladimir Sladek ◽  
Chuan Zeng Zhang
Keyword(s):  
Boundary Integral Equations ◽  
Crack Opening ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Elastic Matrix ◽  
Opening Displacement ◽  
Rigid Disk ◽  
Time Harmonic ◽  
Penny Shaped Crack ◽  
Shaped Inclusion

A 3D time-harmonic problem for an infinite elastic matrix with an arbitrarily located interacting rigid disk-shaped inclusion and a penny-shaped crack is analyzed by the boundary integral equation method. Perfect bonding between the matrix and the moving inclusion is assumed. The crack faces are subjected to time-harmonic loading. The boundary integral equations (BIEs) obtained are solved numerically by the implementation of regularization and discretization procedures. Numerical calculations are carried out for a crack under tensile loading of constant amplitude, where an interacting inclusion is perpendicular to the crack and has the same radius. Both the normal crack-opening-displacement and the mode-I stress intensity factor are investigated for different wave numbers and distances between the crack and the inclusion.

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