The antiplane deformation of a wedge made of a functionally graded material (FGM) with finite radius has been investigated analytically in the present article. In relation to the boundary conditions imposed on the arc portion of the wedge, displacement or traction, two problems have been studied. In each of the problems three various kinds of boundary conditions (traction-displacement, displacement-displacement and traction-traction) have been applied to the radial edges of the wedge. The governing differential equations have been solved by employing finite Fourier transforms and Green’s function method. The closed form solutions for stress and displacement distribution have been achieved for the whole domain. Explicit relations have been extracted for the order of stress singularity in all cases. These relations indicated the dependence of the order of stress singularity on the boundary conditions, material property and wedge angle. In fact, despite of an isotropic wedge, for which the order of stress singularity depends only the geometry of the wedge, in an FG wedge the order of stress singularity depends both the geometry as well as the material property. Manuscript profile

This paper deals with the implementation of an efficient Arbitrary Lagrangian Eulerian (ALE) formulation for the three dimensional finite element modeling of mode I self-similar dynamic fracture process. Contrary to the remeshing technique, the presented algorithm can continuously advance the crack with the one mesh topology. The uncoupled approach is employed to treat the equations. So, each time step is split into two phases: an updated Lagrangian phase followed by an Eulerian phase. The implicit time integration method is applied for solving the transient problem in Lagrangian phase with no convective effects. A mesh motion scheme, in which the related equations need not to be solved at every time step, is proposed in Eulerian phase. The critical dynamic stress intensity factor criterion is used to determine the crack velocity. The variation of dynamic stress intensity factor along the crack front is also studied based on the interaction integral method. The proposed algorithm is applied to investigate the dynamic crack propagation in the DCB specimen subjected to fixed displacement. The predicted results are compared with the experimental study cited in the literature and a good agreement is shown. The proposed algorithm leads to the accurate and efficient analysis of dynamic crack propagation process. Manuscript profile

In the present work the pull-in voltage of a micro cracked cantilever beam subjected to nonlinear electrostatic pressure was studied. Two mathematical models were employed for modeling the problem: a lumped mass model and a classical beam model. The effect of crack in the lumped mass model is the reduction of the effective stiffness of the beam and in the beam model; the crack is modeled as a massless rotational spring the compliance of which is related to the crack depth. Using these two models the pull-in voltage is extracted in the static and dynamic cases. Stability analysis is also accomplished. It has been observed that the pull-in voltage decreases as the crack depth increases and also when the crack approaches the clamped support of the beam. The finding of this research can further be used as a non-destructive test procedure for detecting cracks in micro-beams. Manuscript profile

In this paper, the buckling behavior of stiffened cylindrical shells with initial imperfection under axial loading is numerically studied. The Riks method was used to obtain the nonlinear buckling load and the load-displacement curve. The effect of longitudinal and circumferential stiffeners (stringers and ribs ) was studied on the buckling load as the stiffeners were used separately and together. Also, by considering the shape modes of linear buckling as the initial imperfection, the nonlinear buckling and the sensitivity of the shell to the initial geometric imperfection and its size was investigated.Finally, the using of stiffeners, and the existence of imperfection and their effect on buckling load are presented.It has been observed that the addition of stringer and rib can significantly increase the buckling load, and improve resistance reduction which geometric imperfection caused. As important result, The effect of rib reinforcement does not decrease with increasing initial geometric imperfection, while with increasing geometric imperfection, the effect of string reinforcement decreases. Also, the Snap-Back points observed in the load- displacement curve, indicate the local buckling happened in the shell, during that the strength of the shell is reduced, but the shell still has the ability to withstand under the load and the structure does not fail Manuscript profile