E. Viola¹, F. Tornabene¹, E. Ferretti¹, N. Fantuzzi¹

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.4, pp. 331-369, 2013, DOI:10.3970/cmes.2013.094.331

Abstract In the present paper the Generalized Differential Quadrature Finite Element Method (GDQFEM) is applied to deal with the static analysis of plane state structures with generic through the thickness material discontinuities and holes of various shapes. The GDQFEM numerical technique is an extension of the Generalized Differential Quadrature (GDQ) method and is based on the idea of conventional integral quadrature. In particular, the GDQFEM results in terms of stresses and displacements for classical and advanced plane stress problems with discontinuities are compared to the ones by the Cell Method (CM) and Finite Element Method (FEM). The multi-domain technique is implemented… More >

Changqing Miao¹, Yintao Wei², Xiangqiao Yan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.94, No.1, pp. 29-52, 2013, DOI:10.3970/cmes.2013.094.029

Abstract This paper is concerned with periodic collinear circular-hole cracks in an infinite plate in tension. A numerical approach to this type of circular-hole cracks is presented. Numerical examples are included to illustrate the accuracy of the numerical approach. By means of a generalization of Bueckner's principle and by using a displacement discontinuity method, periodic collinear circular-hole cracks in an infinite plate in tension are investigated in detail by using the numerical approach. Many numerical results are given and discussed. More >

K.-C. Wu², S.-M. Huang², S.-H. Chen³

CMES-Computer Modeling in Engineering & Sciences, Vol.93, No.2, pp. 133-148, 2013, DOI:10.3970/cmes.2013.093.133

Abstract An analysis is presented for an array of collinear cracks subject to a uniform tensile stress wave in an isotropic material. An integral equation for the problem is established by modeling the cracks as distributions of dislocations. The integral equation is solved numerically in the Laplace transform domain first and the solution is then inverted to the time domain to calculate the dynamic stress intensity factors. Numerical examples of one, two, or three collinear cracks are given. The results of one or two cracks are checked to agree closely with the existing results. More >

Y.C. Cai^1,2,3, J. Wu², S.N. Atluri³

CMES-Computer Modeling in Engineering & Sciences, Vol.92, No.1, pp. 63-85, 2013, DOI:10.3970/cmes.2013.092.063

Abstract The numerical manifold method (NMM), based on the finite covers, unifies the continuum analyses and discontinuum analyses without changing a predefined mathematical mesh of the uncracked solid, and has the advantages of being concise in theory as well as being clear in concept. It provides a natural method to analyze complex shaped strong discontinuities as well as weak discontinuities such as multiple cracks, intersecting cracks, and branched cracks. However, the absence of an effective algorithm for cover generation, to date, is still a bottle neck in the research and application in the NMM. To address this issue, a new method… More >

Leiting Dong^1,2, Satya N. Atluri²

CMES-Computer Modeling in Engineering & Sciences, Vol.89, No.5, pp. 417-458, 2012, DOI:10.3970/cmes.2012.089.417

Abstract Two-dimensional weakly-singular Symmetric Galerkin Boundary Elements (SGBEMs) are developed, following the work of [Han and Atluri (2003)], using non-hypersingular integral equations for tractions. Specifically, the present 2D SGBEM is used to compute the stress intensity factors for arbitrary-shaped line cracks, including embedded, edge, branching, and intersecting cracks. The computed stress intensity factors show high accuracy, even with very coarse meshes. The non-collinear mixed-mode fatigue growth analysis of cracks requires a very minimal effort¡ªsimply extending the cracks by adding an element to each crack tip, in the direction of the crack-growth as determined by a physics-based criterion. Moreover, by rearranging the… More >

Yueting Zhou¹, Xing Li², Dehao Yu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.36, No.2, pp. 147-172, 2008, DOI:10.3970/cmes.2008.036.147

Abstract A problem for bonded plane material with a set of curvilinear cracks, which is under the action of a rigid punch with the foundation of convex shape, has been considered in this paper. Kolosov-Muskhelishvili complex potentials are constructed as integral representations with the Cauchy kernels with respect to derivatives of displacement discontinuities along the crack contours and pressure under the punch. The contact of crack faces is considered. The considered problem has been transformed to a system of complex Cauchy type singular integral equations of first and second kind. The presented approach allows to consider various configurations of cracks and… More >

Y. J. Guo¹, J. A. Nairn²

CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.3, pp. 141-156, 2006, DOI:10.3970/cmes.2006.016.141

Abstract This paper describes algorithms for three-dimensional dynamic stress and fracture analysis using the material point method (MPM). By allowing dual velocity fields at background grid nodes, the method provides exact numerical implementation of explicit cracks in a predominantly meshless method. Crack contact schemes were included for automatically preventing crack surfaces from interpenetration. Crack-tip parameters, dynamic$J$-integral vector and mode I, II, and III stress intensity factors, were calculated from the dynamic stress solution. Comparisons to finite difference method (FDM), finite element method (FEM), and boundary element method (BEM), as well as to static theories showed that MPM can efficiently and accurately… More >

Timon Rabczuk¹, Pedro Areias²

CMES-Computer Modeling in Engineering & Sciences, Vol.16, No.2, pp. 115-130, 2006, DOI:10.3970/cmes.2006.016.115

Abstract This paper proposes a meshfree method for arbitrary evolving cracks in thin shells. The approach is an improvement of the method proposed by Rabczuk T., Areias P.M.A., Belytschko T. (A meshfree thin shell for large deformation, finite strain and arbitrary evolving cracks, International Journal for Numerical Methods in Engineering). In the above cited paper, a shell was developed based on an intrinsic basis of third order completeness. Third order completeness was necessary to remove membrane locking. This resulted in the use of very large domains of influence that made the method computationally expensive. If the crack was modelled by a… More >

A. Dimitrov¹, F.-G. Buchholz², E. Schnack³

CMES-Computer Modeling in Engineering & Sciences, Vol.12, No.1, pp. 1-26, 2006, DOI:10.3970/cmes.2006.012.001

Abstract Crack propagation in 3D-structures cannot be reduced (in general) to a series of plane problems along the crack front edge, due to the existence of some "corners'' on the crack front, where the elastic fields are of a real three-dimensional nature. The most important example for such a corner ist the point, where the crack front intersects a free surface of the body. According to the concept of weak and strong singularities, it is possible to obtain the asymptotics for the stress intensity factor (SIF) as well as the strain energy release rate (SERR) in the neighborhood of such a… More >

G. Cocchetti², G. Maier², X. P. Shen³

CMES-Computer Modeling in Engineering & Sciences, Vol.3, No.3, pp. 279-298, 2002, DOI:10.3970/cmes.2002.003.279

Abstract Interface models mean here relationships between displacement jumps and tractions across a locus of displacement discontinuities. Frictional contact and quasi-brittle fracture interpreted by cohesive crack models are typical mechanical situations concerned by the present unifying approach. Plastic-softening multidissipative interface models are studied in piecewise linear formats, i.e. assuming linearity for yield functions, plastic potentials and relationships between static and kinematic internal variables. The properties and the pros and cons of such simplified models in a variety of formulations (fully non-holonomic in rates, holonomic and in finite steps), all mathematically described as linear complementarity problems, are comparatively investigated in view of… More >