Bing Li^1,2, Hongbo Dong¹

CMES-Computer Modeling in Engineering & Sciences, Vol.84, No.3, pp. 205-228, 2012, DOI:10.3970/cmes.2012.084.205

Abstract Different from single crack identification method, the number of cracks should be firstly identified, and then the location and depth of each crack can be predicted for multiple cracks identification technology. This paper presents a multiple crack identification algorithm for rotor using wavelet finite element method. Firstly, the changes in natural frequency of a structure with various crack locations and depths are accurately obtained by means of wavelet finite element method; and then the damage coefficient method is used to determine the number and region of cracks. Finally, by finding the points of intersection of three frequency contour lines in… More >

Yue-Ting Zhou¹, Xing Li², De-Hao Yu³, Kang Yong Lee^1,4

CMES-Computer Modeling in Engineering & Sciences, Vol.63, No.2, pp. 163-190, 2010, DOI:10.3970/cmes.2010.063.163

Abstract In this paper, a coupled crack/contact model is established for the composite material with arbitrary periodic cracks indented by periodic punches. The contact of crack faces is considered. Frictional forces are modeled to arise between the punch foundation and the composite material boundary. Kolosov-Muskhelisvili complex potentials with Hilbert kernels are constructed, which satisfy the continuity conditions of stress and displacement along the interface identically. The considered problem is reduced to a system of singular integral equations of first and second kind with Hilbert kernels. Bounded functions are defined so that singular integral equations of Hilbert type can be transformed to… More >

C. Becker¹, S. Jox², G. Meschke³

CMES-Computer Modeling in Engineering & Sciences, Vol.57, No.3, pp. 245-278, 2010, DOI:10.3970/cmes.2010.057.245

Abstract A three-dimensional numerical model based on the Extended Finite Element Method (X-FEM) is presented for the simulation of cohesive cracks in cementitious materials, such as concrete, in a hygro-mechanical framework. Enhancement functions for the small scale resolution of the displacement jump across cracks in the context of the X-FEM is used in conjunction with a higher order family of hierarchical shape functions for the representation of the large scale displacement field of the investigated structure. Besides the theoretical and computational formulation in a multiphase context, aspects of the implementation, such as integration and crack tracking algorithms, are discussed. Representative numerical… More >

Sheng-Hu Ding^1,2, Xing Li², Yue-Ting Zhou^2,3

CMES-Computer Modeling in Engineering & Sciences, Vol.56, No.1, pp. 43-84, 2010, DOI:10.3970/cmes.2010.056.043

Abstract In this paper, the crack-tip fields in bonded functionally graded finite strips are studied. Different layers may have different nonhomogeneity properties in the structure. A bi-parameter exponential function was introduced to simulate the continuous variation of material properties. The problem was reduced as a system of Cauchy singular integral equations of the first kind by Laplace and Fourier integral transforms. Various internal cracks and edge crack and crack crossing the interface configurations are investigated, respectively. The asymptotic stress field near the tip of a crack crossing the interface is examined and it is shown that, unlike the corresponding stress field… More >

Chein-Shan Liu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.40, No.1, pp. 1-28, 2009, DOI:10.3970/cmes.2009.040.001

Abstract We consider an inverse problem of Laplace equation by recoverning boundary value on the inner circle of a two-dimensional annulus from the overdetermined data on the outer circle. The numerical results can be used to determine the Robin coefficient or crack's position inside a disk from the measurements of Cauchy data on the outer boundary. The Fourier series is used to formulate the first kind Fredholm integral equation for the unknown data f(θ) on the inner circle. Then we consider a Lavrentiev regularization, by adding an extra term αf(θ) to obtain the second kind Fredholm integral equation. The termwise separable… More >

P.H. Wen¹, M.H. Aliabadi², Y.W. Liu³

CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.3, pp. 133-148, 2008, DOI:10.3970/cmes.2008.030.133

Abstract Based on the variation of potential energy, the element-free Galerkin method (MFGM) has been investigated for structures with crack on the basis of radial base function interpolation. An enriched radial base function is introduced to capture the singularities of stress at the crack tips. The advantages of the finite element method are remained in this method and there is a significant improvement of accuracy, particularly for the crack problems of fracture mechanics. The applications of the element-free Galerkin method with enriched radial base function to two-dimensional fracture mechanics in functionally graded materials have been presented and comparisons have been made… More >

Q. Ma¹, C. Levy², M. Perl³

CMES-Computer Modeling in Engineering & Sciences, Vol.29, No.2, pp. 95-110, 2008, DOI:10.3970/cmes.2008.029.095

Abstract Networks of radial and longitudinally-coplanar, internal, surface cracks are typical in rifled, autofrettaged, gun barrels. In two previous papers, the separate effects of large arrays of either radial or longitudinally-coplanar semi-elliptical, internal, surface cracks in a thick-walled, cylindrical, pressure vessel under both ideal and realistic autofrettage were studied. When pressure is considered solely, radial crack density and longitudinal crack spacing were found to have opposing effects on the prevailing stress intensity factor, K_IP. Furthermore, the addition of the negative stress intensity factor (SIF), K_IA, resulting from the residual stress field due to autofrettage, whether ideal or realistic, tended to decrease… More >

G.F. Karlis¹, S.V. Tsinopoulos², D. Polyzos³, D.E. Beskos⁴

CMES-Computer Modeling in Engineering & Sciences, Vol.26, No.3, pp. 189-208, 2008, DOI:10.3970/cmes.2008.026.189

Abstract A boundary element method, suitable for solving two and three dimensional gradient elastic fracture mechanics problems under static loading, is presented. A simple gradient elastic theory (a simplied version of Mindlin's Form-II general theory of gradient elasticity) is employed and the static gradient elastic fundamental solution is used to construct the boundary integral representation of the problem with the aid of a reciprocal integral identity. In addition to a boundary integral representation for the displacement, a boundary integral representation for its normal derivative is also necessary for the complete formulation of a well-posed problem. Surface quadratic line and quadrilateral boundary… More >

Daiki Shiozawa¹, Shiro Kubo², Takahide Sakagami², Masaaki Takagi²

CMES-Computer Modeling in Engineering & Sciences, Vol.11, No.1, pp. 27-36, 2006, DOI:10.3970/cmes.2006.011.027

Abstract The passive electric potential CT (computed tomography) method using piezoelectric film was applied to the identification of plural through cracks. The use of piezoelectric material made it possible to obtain electric potential field without applying electric current. For identification of cracks an inverse analysis scheme based on the least residual method was applied, in which square sum of residuals is evaluated between the measured electric potential distributions and those computed by using the finite element method. Akaike information criterion (AIC) was used to estimate the number of cracks. Numerical simulations were carried out on the identification of plural cracks and… More >

U. Andreaus^1,3, R.C. Batra², M. Porfiri^{2, 3}

CMES-Computer Modeling in Engineering & Sciences, Vol.9, No.2, pp. 111-132, 2005, DOI:10.3970/cmes.2005.009.111

Abstract Structural health monitoring techniques based on vibration data have received increasing attention in recent years. Since the measured modal characteristics and the transient motion of a beam exhibit low sensitivity to damage, numerical techniques for accurately computing vibration characteristics are needed. Here we use a Meshless Local Petrov-Galerkin (MLPG) method to analyze vibrations of a beam with multiple cracks. The trial and the test functions are constructed using the Generalized Moving Least Squares (GMLS) approximation. The smoothness of the GMLS basis functions requires the use of special techniques to account for the slope discontinuities at the crack locations. Therefore, a… More >