Dual boundary element method for axisymmetric crack analysis

In this paper a dual boundary element formulation is developed and applied to the evaluation of stress intensity factors in, and propagation of, axisymmetric cracks. The displacement and stress boundary integral equations are reviewed and the asymptotic behaviour of their singular and hypersingular kernels is discussed. The modified crack closure integral method is employed to evaluate the stress intensity factors. The combination of the dual formulation with this method requires the adoption of an interpolating function for stresses after the crack tip. Different functions are tested under a conservative criterion for the evaluation of the stress intensity factors. A crack propagation procedure is implemented using the maximum principal stress direction rule. The robustness of the technique is assessed through several examples where results are compared either to analytical ones or to BEM and FEM formulations.     

Frictional contact analysis of multiple cracks by incremental displacement and resultant traction boundary integral equations

Based on the merits of the dual boundary element technique, a modified dual boundary element technique is extended to deal with the frictional contact of a finite plate with arbitrarily distributed multiple cracks. Besides establishing the incremental displacement boundary integral equation on the outer boundary, the resultant traction boundary integral equation on one of the crack surfaces is also developed. Since the resultant traction instead of incremental traction on the crack surface is introduced, the computed resultant contact tractions under sliding condition satisfy the Coulomb's friction law directly. Hence, as compared with the authors' previous work, only very few computation iterations are required by this method to accurately describe the contact situations of crack surfaces. As a result, not only the linear cracks, but also other types of multiple cracks, for example, curved and kinked cracks, can be tackled. The effects of friction and interaction among cracks on the computation of stress intensity factors are also displayed.     

A three-dimensional boundary element formulation for the elastoplastic analysis of cracked bodies

In this paper a general boundary element formulation for the three-dimensional elastoplastic analysis of cracked bodies is presented. The non-linear formulation is based on the Dual Boundary Element Method. The continuity requirements of the field variables are fulfilled by a discretization strategy that incorporates continuous, semi-discontinuous and discontinuous boundary elements as well as continuous and semi-discontinuous domain cells. Suitable integration procedures are used for the accurate integration of the Cauchy surface and volume integrals. The explicit version of the initial strain formulation is used to satisfy the non-linearity. Several examples are presented to demonstrate the application of the proposed method. © 1998 John Wiley & Sons, Ltd.     

Dual boundary element method for anisotropic dynamic fracture mechanics

In this work, the dual boundary element method formulation is developed for effective modelling of dynamic crack problems. The static fundamental solutions are used and the domain integral, which comes from the inertial term, is transformed into boundary integrals using the dual reciprocity technique. Dynamic stress intensity factors are computed from crack opening displacements. Comparisons are made with quasi‐isotropic as well as anisotropic results, using the sub‐region technique. Several examples are presented to assess the accuracy and efficiency of the proposed method. Copyright © 2004 John Wiley & Sons, Ltd.     

An efficient dual boundary element technique for a two-dimensional fracture problem with multiple cracks

An efficient dual boundary element technique for the analysis of a two-dimensional finite body with multiple cracks is established. In addition to the displacement integral equation derived for the outer boundary, since the relative displacement of the crack surfaces is adopted in the formulation, only the traction integral equation is established on one of the crack surfaces. For each crack, a virtual boundary is devised and connected to one of the crack surfaces to construct a closed integral path. The rigid body translation for the domain enclosed by the closed integral path is then employed for evaluating the hypersingular integral. To solve the dual displacement/traction integral equations simultaneously, the constant and quadratic isoparametric elements are taken to discretize the closed integral paths/crack surfaces and the outer boundary, respectively. The present method has distinct computational advantages in solving a fracture problem which has arbitrary numbers, distributions, orientations and shapes of cracks by a few boundary elements. Several examples are analysed and the computed results are in excellent agreement with other analytical or numerical solutions.     

Boundary element analysis of three‐dimensional cracks in anisotropic solids

This paper presents a boundary element analysis of linear elastic fracture mechanics in three‐dimensional cracks of anisotropic solids. The method is a single‐domain based, thus it can model the solids with multiple interacting cracks or damage. In addition, the method can apply the fracture analysis in both bounded and unbounded anisotropic media and the stress intensity factors (SIFs) can be deduced directly from the boundary element solutions. The present boundary element formulation is based on a pair of boundary integral equations, namely, the displacement and traction boundary integral equations. While the former is collocated exclusively on the uncracked boundary, the latter is discretized only on one side of the crack surface. The displacement and/or traction are used as unknown variables on the uncracked boundary and the relative crack opening displacement (COD) (i.e. displacement discontinuity, or dislocation) is treated as a unknown quantity on the crack surface. This formulation possesses the advantages of both the traditional displacement boundary element method (BEM) and the displacement discontinuity (or dislocation) method, and thus eliminates the deficiency associated with the BEMs in modelling fracture behaviour of the solids. Special crack‐front elements are introduced to capture the crack‐tip behaviour. Numerical examples of stress intensity factors (SIFs) calculation are given for transversely isotropic orthotropic and anisotropic solids. For a penny‐shaped or a square‐shaped crack located in the plane of isotropy, the SIFs obtained with the present formulation are in very good agreement with existing closed‐form solutions and numerical results. For the crack not aligned with the plane of isotropy or in an anisotropic solid under remote pure tension, mixed mode fracture behavior occurs due to the material anisotropy and SIFs strongly depend on material anisotropy. Copyright © 2000 John Wiley & Sons, Ltd.     

Singular boundary elements for the analysis of cracks in plane strain

Straight and curved cracks are modelled by direct formulation boundary elements, of geometry defined by Hermitian cubic shape functions. Displacement and traction are interpolated by the Hermitian functions, supplemented by singular functions which multiply stress intensity factors corresponding to the dominant modes of crack opening in which displacement is proportional to the square root of distance r from the crack tip, and subdominant modes in which it is proportional to r^1·5. The singular functions extend over many boundary elements on each crack face. A nodal collocation scheme is used, in which additional boundary integral equations are obtained by differentiation of the equation obtained from Betti's theorem. The hypersingular kernels of the equations so derived are integrated by consideration of trial displacement fields of subdomains lying to either side of the crack. Examples are shown of the analysis of buried and edge cracks, to demonstrate the effects of modelling subdominant modes and extending singular shape functions over many elements.     

Dual boundary element analysis for fatigue behavior of missile structures

Abstract

The fatigue behavior of a crack in a missile structure is studied using the dual boundary integral equations developed by Hong and Chen (1988). This method, which incorporates two independent boundary integral equations, uses the displacement equation to model one of the crack boundaries and the traction equation to the other. A single domain approach can be performed efficiently. The stress intensity factors are calculated and the paths of crack growth are predicted. In order to evaluate the results of dual BEM, four examples with FEM results are provided. Two practical examples, cracks in a V‐band and a solid propellant motor are studied and are compared with experimental data. Good agreement is found.     

A variational technique for boundary element analysis of 3D fracture mechanics weight functions: static

The dual boundary element method coupled with the weight function technique is developed for the analysis of three-dimensional elastostatic fracture mechanics mixed-mode problems. The weight functions used to calculate the stress intensity factors are defined by the derivatives of traction and displacement for a reference problem. A knowledge of the weight functions allows the stress intensity factors for any loading on the boundary to be calculated by means of a simple boundary integration without singularities. Values of mixed-mode stress intensity factors are presented for an edge crack in a rectangular bar and a slant circular crack embedded in a cylindrical bar, for both uniform tensile and pure bending loads applied to the ends of the bars. © 1998 John Wiley & Sons, Ltd.     

Using the boundary element method to solve rolling contact problems

A new approach to steady-state rolling, with and without force transmission, based on the boundary element method is presented. The proposed formulation solves the problem in a more general way than semi-analytical methods, with which it shares some approximations. The robustness and accuracy of the proposed method is reflected in the comparative analysis of the results obtained for three different types of rolling problems involving identical, dissimilar and tyred cylinders, respectively.     

Dual boundary element method for three-dimensional thermoelastic crack problems

This paper describes the formulation and numerical implementation of the three-dimensional dual boundary element method (DBEM) for the thermoelastic analysis of mixed-mode crack problems in linear elastic fracture mechanics. The DBEM incorporates two pairs of independent boundary integral equations; namely the temperature and displacement, and the flux and traction equations. In this technique, one pair is applied on one of the crack faces and the other pair on the opposite one. On non-crack boundaries, the temperature and displacement equations are applied. This revised version was published online in July 2006 with corrections to the Cover Date.     

An indirect boundary element method for three-dimensional dynamic fracture mechanics

Indirect boundary element methods (fictitious load and displacement discontinuity) have been developed for the analysis of three-dimensional elastostatic and elastodynamic fracture mechanics problems. A set of boundary integral equations for fictitious loads and displacement discontinuities have been derived. The stress intensity factors were obtained by the stress equivalent method for static loading. For dynamic loading the problem was studied in Laplace transform space where the numerical calculation procedure, for the stress intensity factor K_I(p), is the same: as that for the static problem. The Durbin inversion method for Laplace transforms was used to obtain the stress intensity factors in the time domain K_I(t). Results of this analysis are presented for a square bar, with either a rectangular or a circular crack, under static and dynamic loads.     

A time‐dependent formulation of dual boundary element method for 3D dynamic crack problems

In this paper, the dual boundary element method in time domain is developed for three‐dimensional dynamic crack problems. The boundary integral equations for displacement and traction in time domain are presented. By using the displacement equation and traction equation on crack surfaces, the discontinuity displacement on the crack can be determined. The integral equations are solved numerically by a time‐stepping technique with quadratic boundary elements. The dynamic stress intensity factors are calculated from the crack opening displacement. Several examples are presented to demonstrate the accuracy of this method. Copyright © 1999 John Wiley & Sons, Ltd     

The boundary element analysis of cracked stiffened sheets,reinforced by adhesively bonded patches

This paper presents a formulation based on the Dual Boundary Element Method and on the Dual Reciprocity Method for the analysis of thin cracked metal sheets to which thin metal patches and stiffeners are adhesively bonded. The stiffened cracked sheet is modelled with the Dual Boundary Element Method. Adhesive shear stresses are modelled as action–reaction body forces exchanged by the sheet and patches. The Dual Reciprocity Method is used to avoid the discretization of the patches attachment domain into internal cells. Several examples are presented to demonstrate the efficiency and robustness of the method developed. The examples include sheets with embedded or edge cracks, stiffened or not, to which single or double patches are adhesively bonded. © 1998 John Wiley & Sons, Ltd.     

A linear programming formulation for incremental contact analysis

A novel algorithm for the analysis of contact problems in elasticity has been presented in this paper. The algorithm is based on the boundary element method and a direct approximation of the contact complementarity conditions using linear programming. An incremental loading scheme has been developed to ensure an accurate approximation of the deformation path that the object experiences during the process of contact. Several numerical examples have been analysed to illustrate the validity of the proposed formulations.     

Stress analysis with arbitrary body force by boundary element method

Linear stress analysis without body force can be easily carried out by means of the boundary element method. Some cases of linear stress analysis with body force can also be solved without the domain integral. However domain integrals are generally necessary to solve the linear stress problems with complicated body forces. This paper shows that the linear stress problems with complicated body forces can be solved approximately without the domain integral. In order to solve these problems, the domain is divided into small areas using contour lines of body force. In these areas, the distributions of body force are assumed approximately to satisfy the Laplace equation.     

Stiffened cracked plates analysis by dual boundary element method

In this paper a boundary element formulation for analysis of shear deformable stiffened cracked plates is presented. By coupling boundary element formulation of shear deformable plate and two dimensional plane stress elasticity, dual boundary integral equations are presented. The interaction forces between stiffeners and the plate are treated as line distributed body forces along the attachment. Both concentric and eccentric stiffeners have been considered. Rectangular stiffened plate containing a single crack and double cracks subjected to uniform distributed moment on the crack surface and uniform shear load on the plate are analysed by the proposed method. Good agreement has been achieved compared with analytical solutions.     

Three dimensional boundary element analysis of internal cracks under sliding contact load with a spherical indenter

Using boundary element based three dimensional modelling for linear fracture mechanics, we present an analysis of cracking in a homogeneous medium subject to contact load. The proposed iterative solution procedure allows a simultaneous treatment of a reasonable number of partially closed cracks. It is shown that the most probable direction of propagation of a vertical internal crack is strongly dependent on its size compared to the contact radius and its location with respect to the axis of maximum normal load.     

A new generation of boundary element methods in fracture mechanics

In this paper the dual boundary element methods for the analysis of crack problems in fracture mechanics is presented. The formulations described include: elastostatic, thermoelastic, elastoplastic and elastodynamic. Also presented are formulations relating to anisotropic and concrete materials. Particular attention is given to crack growth modelling. Examples are presented to demonstrate the capability and robustness of this new generation of boundary element methods. This revised version was published online in July 2006 with corrections to the Cover Date.     

Plastic,viscoplastic and creep fracture problems with the boundary element method

The present paper shows the applicability of the dual boundary element method to analyse plastic, viscoplastic and creep behaviours in fracture mechanics problems. Several models with a crack, including a square plate, a holed plate and a notched plate, are analysed. Special attention is taken when the discretization of the domain is performed. In fact, for the plasticity and viscoplasticity cases, only the region susceptible to yielding was discretized, whereas the creep case required the discretization of the whole domain. The proposed formulation is presented as an alternative technique to study these kinds of nonlinear problems. Results from the present formulation are compared to those of the well‐established finite element technique, and they are in good agreement. Important fracture mechanic parameters like K_I, K_II, J‐integrals and C‐integrals are also included. In general, the results, for the plastic, viscoplastic and creep cases, exhibit that the highest stress concentrations are in the vicinity of the crack tip and they decrease as the distance from the crack tip is increased.