Cracks cause to change dynamic response of beams and make discontinuity in slope of the deflection of the beams. The dynamic analysis of the Euler-Bernoulli Cracked beam on the elastic foundation subjected to the concentrated load is presented in this paper. The stiffness of the elastic foundation and elastic supports influence on vibrational characteristics of the Cracked beam. The Dynamic Green Function is applied to solve the governing equation. Thus, the dynamic response of the Cracked beam is determined by Laplace Transform method. The effects of depth and location of the crack on natural frequency and deflection of the Cracked beam on an elastic foundation are evaluated. In order to demonstrate the capability of the present approach, several numerical examples are worked out and the results are discussed.

In this article, the size effect on the dynamic behavior of a simply supported Multi-Cracked microbeam is studied based on Modified Couple Stress Theory (MCST). At first, based on MCST, the equivalent torsional stiffness spring for every open edge crack at its location is calculated; in this regard, the Stress Intensity Factor (SIF) is also considered for all open edge cracks. Hamilton’ s principle has been used in order to achieve the governing equations of motion of the system and associated boundary conditions are derived based on MCST. Then the natural frequencies of Multi-Cracked microbeam are analytically determined. After that, the Numerical solutions have been presented for the microbeam with two open edge cracks. Finally, the variation of the first three natural frequencies of the system is investigated versus different values of the depth and the location of two cracks and the material length scale parameter. The obtained results express that the natural frequencies of the system increase by increasing the material length scale parameter and decrease by moving away from the simply supported of the beam and node points, in addition to increasing the number of cracks and cracks depth.

In this paper, 2D boundary element stress analysis is carried out to obtain the T-stress for Multiple internal edge cracks in thick-walled cylinders for a wide range of cylinder radius ratios and relative crack depth. The T-stress, together with the stress intensity factor K, provides a more reliable two-parameter prediction of fracture in linear elastic fracture mechanics. T-stress weight functions are then derived from the T-stress solutions for two reference load conditions corresponding to the cases when the Cracked cylinder is subject to a uniform and to a linear applied stress variation on the crack faces. The derived weight functions are then verified for several non-linear load conditions. Using the BEM results as reference T-stress solutions; the T-stress weight functions for thick-walled cylinder have also been derived. Excellent agreements between the BEM results and weight function predictions are obtained. The weight functions derived are suitable for obtaining Tstress solutions for the corresponding Cracked thick-walled cylinder under any complex stress fields. Results of the study show that the two dimensional BEM analysis, together with weight function method, can be used to provide a quick and accurate estimate of T-stress for 2-D crack problems.

This paper devoted to analysis of Cracked truss type structures. For this purpose, five common Cracked bar finite elements, according to the laws of fracture mechanics, are first introduced and verified. Parameters which affect the stiffness matrix of the Cracked element are also evaluated. In this paper, a procedure for calculation of stress intensity factor (SIF) by employing Cracked element is proposed. A simple Cracked truss structure is finally studied. Furthermore, this article could be considered as a relatively comprehensive source of the common Cracked bar elements.

The dual boundary element method is formulated for the analysis of linear elastic Cracked plates. The dual boundary integral equations of the method are the displacement and the traction equations. When these equations are simultaneously applied along the crack boundaries, general crack problems can be solved in a single-region formulation, with both crack boundaries discretized with discontinuous boundary elements. The stress intensity factors evaluation is carried out by the J-integral decomposition method which is applied on a circular path, defined around each crack tip. Examples of geometries with edge, and embedded cracks are analyzed. The accuracy and efficiency of the dual boundary element method and the J-integral make the present formulation ideal for the study of Cracked plates.

This paper focuses on using the recently developed extended finite element model for buckling analysis of edge Cracked columns under concentric axial load. The effect of crack depth and its location on the carrying capacity of columns is studied. The effect of different boundary conditions is also investigated. Numerical examples are offered to show the efficiency and effectiveness of the proposed method. The presented results are compared with analytical and experimental works available in the literature. Good agreement with experiments is shown, although the difference with analytical results is considerable for columns with deeper cracks. The reason of this difference is discussed. It is shown that the proposed method is more accurate than the analytical methods which are developed based on rotational spring models.