P. Fedelinski

The dual boundary element method:Ĵ-integral for dynamic stress intensity factors

The application of the dual boundary element method and the path independentĴ-integral for the evaluation of dynamic stress intensity factors of stationary cracks in a linear elastic material is presented. The distinct set of boundary equations of elastodynamics is obtained by using the dual boundary element method and the dual reciprocity approach. Numerical implementation of the path-independentĴ-integral and the decomposition technique is presented. The method is applied for several cracked structures and the results are compared with solutions obtained by using other methods.

A single-region time domain BEM for dynamic crack problems

Abstract A time domain boundary element method, which allows the analysis of dynamic crack problems by using a single-region formulation, is presented. The present method generates the distinct set of boundary integral equations by applying the displacement equation to one of the crack surfaces and the traction equation to the other. The boundary of the structure is divided into continuous, semi-discontinuous and discontinuous quadratic elements. The temporal variation of boundary displacements and tractions is approximated by piecewise linear and constant functions, respectively. The dynamic stress intensity factors are calculated using the crack opening displacements and the path independent Ĵ-integral. This method is used to study dynamic behaviour of stationary cracks in finite and infinite domains in two-dimensional analysis. The results for two examples are compared with other reported solutions, showing good agreement.

The laplace transform DBEM for mixed-mode dynamic crack analysis

A boundary element method (BEM) for the two-dimensional analysis of structures with stationary cracks subjected to dynamic loads is presented. The difficulties in modelling the structures with cracks by BEM are solved by using two different equations for coincident points on the crack surfaces. The equations are the displacement and the traction boundary integral equations. This method of analysis requires discretization of the boundary and the crack surfaces only. The time-dependent solutions are obtained by the Laplace transform method, which is used to solve several examples. The influence of the number of boundary elements and the number of Laplace parameters is investigated and a comparison with other reported solutions is shown.

The dual boundary element method in dynamic fracture mechanics

Abstract A boundary element formulation, which does not require domain integration, is presented for a general dynamic crack problem in a linear elastic material. The problem is solved using the dual boundary element method, that is, the displacement equation is applied to one of the crack surfaces and the traction equation to the other. Domain integrals in the elastodynamic equation are transformed into boundary integrals using the dual reciprocity method. As the result of the discretization a set of ordinary differential equations in time is obtained. Several numerical examples are considered, showing good agreement with the results given by other methods.

Boundary element formulations for the dynamic analysis of cracked structures

Boundary element methods, which allow the analysis of dynamic crack problems with a single-region formulation are presented. All the methods generate a distinct set of boundary integral equations by specifying the displacement equation on one crack surface and the traction equation on the other. This technique is combined with a time domain formulation, a Laplace transform formulation or the dual reciprocity method. Dynamic stress intensity factors are calculated using the quarter-point elements and a path independent J-integral. These methods are used to study dynamic behaviour of stationary cracks in finite domains and in two-dimensions. The three approaches are applied to a mixed-mode crack problem. Formulation details of the methods and computational efficiency as characterized by memory, time requirements and accuracy are subsequently discussed and compared.

Dual reciprocity boundary element method in Laplace domain applied to anisotropic dynamic crack problems

In this paper the dual reciprocity boundary element method in the Laplace domain for anisotropic dynamic fracture mechanic problems is presented. Crack problems are analyzed using the subregion technique. The dynamic stress intensity factors are computed using traction singular quarter-point elements positioned at the tip of the crack. Numerical inversion from the Laplace domain to the time domain is achieved by the Durbin method. Numerical examples of dynamic stress intensity factor evaluation are considered for symmetric and non-symmetric problems. The influence of the number of Laplace parameters and internal points in the solution is investigated.

THE TIME-DOMAIN DBEM FOR RAPIDLY GROWING CRACKS

The time-domain Dual Boundary Element Method (DBEM) is developed to analyse rapidly growing cracks in structures subjected to dynamic loads. Two-dimensional problems, where the velocity of the crack growth is constant and the path is not predefined are studied. The present method uses the dual boundary formulation, i.e. the displacement and the traction boundary integral equations to obtain the solution by discretizing the boundary of the body and the crack surfaces only. The crack growth is modelled by adding new elements ahead of the crack tip. It is assumed that the direction of the increment is perpendicular to the direction of maximum circumferential stress. The method is used to analyse growing cracks in infinite sheet and finite plates, and the results are compared with other reported solutions, showing good agreement.

Free vibration analysis of anisotropic material structures using the boundary element method

This paper presents a formulation for the analysis of free vibration in anisotropic structures using the boundary element method. The fundamental solution for elastostatic is used and the inertial terms are treated as body forces providing domain integrals. The dual reciprocity boundary element method is used to reduce domain integrals to boundary integrals. Mode shapes and natural frequencies for free vibration of orthotropic structures are obtained and compared with finite element results showing good agreement.

Boundary elements in shape design sensitivity analysis and optimal design of vibrating structures

Abstract A general approach to shape design sensitivity analysis and optimal design for dynamic transient and free vibrations problems using boundary elements is presented. The material derivatives and the adjoint system method are applied to obtain first-order sensitivities for the effect of boundary shape variations. A numerical example of shape sensitivity analysis and optimal design for free vibrations of an elastic body is presented.

Integral formulation for elastodynamic T-stresses

In this paper, a path independent integral formulation is presented for the computation of dynamic T-stresses in a two-dimensional body with a stationary crack. The mutual M-integral expressed through dynamic Ĵ-integrals provides sufficient information for determining T-stresses on the basis of the relationship found between the M-integral and T-stresses. The elastodynamic fields required for the evaluation of the Ĵ-and M-integrals are obtained by the boundary element method. The time-domain approach is used for the solution of the boundary value crack problem and numerical results for two crack problems are presented. In the first a rectangular plate with a central crack is considered and in the second two cracks at a hole in an infinite sheet. A comparison is made with the results obtained by the boundary layer and displacement field methods based on the asymptotic expansions of stresses and displacements at a crack tip vicinity.