M.H. Aliabadi

Decomposition of the mixed-mode J-integral—revisited

In this paper the correct decomposition of three-dimensional stress and displacement fields for decoupling the mixed mode J-integral into mode I, II and III is presented. It is believed that this has not been achieved before as certain components for the correct derivation have been missing. It is shown that by using the correct decomposition method, a different area integral for the mode II and III J-integrals is obtained. Several test examples are presented to demonstrate the accuracy of the method.

The boundary element method applied to time dependent problems in anisotropic materials

In this paper a multi-domain boundary element formulation is developed for the solution of two-dimensional dynamic anisotropic problems with or without cracks. The inertia effects are treated as body forces and the dual reciprocity formulation is used to transform the domain integral into a boundary integral. In fracture problems, traction singular quarter point elements are used in order to give a correct representation of displacement and traction fields around the crack tip. The dynamic stress intensity factors are computed directly from the tractions at the crack tip node. The results obtained demonstrate good agreement with other reported results and show strong dependence on the material anisotropy.

Hypersingular boundary element formulation for Reissner plates

In this work, the hypersingular boundary element formulation for plate bending analysis based on Reissner theory is presented. First order Taylor expansion are used to deal with the strong singularity O(1/r), whereas, rigid body considerations together with the Taylor expansion are used to compute the hypersingular kernels O(l/r2). The plate boundary is discretised into quadratic isoparametric discontinuous boundary elements to satisfy the continuity requirements for the boundary unknowns. Several examples are tested, including thin and thick plates. The results show a good agreement with both the analytical solutions and the corresponding results for the standard displacement boundary element formulation.

On the solution of three-dimensional thermoelastic mixed-mode edge crack problems by the dual boundary element method

Abstract 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. 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 on the opposite one. On non-crack boundaries, the temperature and displacement equations are applied. Special shape functions are implemented to model the r behaviour of crack tip fields. Stress intensity factors were calculated with the crack opening displacement formulae and by using standard and special elements at the crack front. To demonstrate the accuracy and efficiency of the proposed method, several examples were solved and the results compared, where possible, with existing solutions.

Boundary element analysis of two-dimensional elastoplastic contact problems

Abstract A general boundary element formulation for contact problems, capable of dealing with local elastoplastic effects and friction, is presented. Both conforming and non-conforming problems may be analysed. The contact problem is solved by means of a direct constraint technique, in which compatibility and equilibrium conditions are directly enforced in the general system of equations. The contact areas are modelled with linear interpolation functions, and quadratic interpolation functions are used everywhere else. Elastoplasticity is solved by a BEM initial strain approach The Von Mises yield criterion with its associated flow rule is adopted. Both perfectly plastic and work hardening materials are studied in the proposed formulation. An incremental loading technique is proposed, which allows accurate development of the loading history of the problem. The non-linear nature of these problems demands the use of an iterative procedure, to determine the correct frictional conditions at every node of the contact area and the value of the plastic strains at selected points where local yielding may have occurred. Several numerical examples are presented to demonstrate the efficiency of the proposed formulation.

Mixed-mode weight functions in three-dimensional fracture mechanics: dynamic

Abstract In this paper, the indirect boundary element method, coupled with the weight function concept, is developed for the analysis of three-dimensional elastostatic fracture mechanics mixed-mode problems. A set of boundary integral equations for the fictitious loads and the displacement discontinuities are derived. The weight functions used to calculate the stress intensity factors are determined by incrementing the crack front over a small region. The stress intensity factors were also evaluated by the equivalent stress method to compare with those obtained from the weight functions. Results of mixed-mode stress intensity factors are presented for a square bar, with either a rectangular or a circular crack, under static load.

Boundary element analysis of foundation plates in buildings

In this paper, a boundary element method for analyzing building foundation plates is presented. The shear deformation is considered using the Reissner plate theory. The Winkler model is used to model the behavior of the soil. Only the boundary of the plate needs to be discretized. Two practical applications are solved and the results are compared to alternative solutions of different methods, such as, finite difference, finite element and 3D boundary element methods.

A contour integral for three-dimensional crack elastostatic analysis☆

A contour integral method for calculating stress intensity factors has been successfully applied to two-dimensional crack problems for both static and dynamic cases. In this paper the method is extended to three-dimensional static problems. By means of the displacement discontinuity method and the technique of variation of crack area, the required derivatives of traction and displacement for a reference problem are determined. The stress intensity factors are calculated by a contour integral with a non-singular integrand. The only absolute values of traction and displacement that are required for the real problem are on contours away from the crack-tip; they are determined by the dual boundary element method. For mixed-mode problems, the ratios of stress intensity factors are determined by the ratios of the mixed-mode discontinuity displacements near the crack front, all stress intensity factors can be calculated from only one reference solution.