Papers by Keyword: Finite Element Alternating Method FEAM

Abstract: The finite element alternating method (FEAM) was extended to obtain fracture mechanics parameters and elasto-plastic stress fields for 3-D inner cracks. For solving a problem of a 3-D finite body with cracks, the FEAM alternates independently the finite element method (FEM) solution for the uncracked body and the solution for the crack in an infinite body. As the required solution for a crack in an infinite body, the symmetric Galerkin boundary element method formulated by Li and Mear was used. For elasto-plastic numerical analysis, the initial stress method proposed by Zienkiewicz and co-workers and the iteration procedure proposed by Nikishkov and Atluri were used after modification. The extended FEAM was examined through comparing with the results of commercial FEM program for several example 3-D crack problems.

Abstract: The finite element alternating method (FEAM), in conjunction with the finite element analysis (FEA) and the analytical solution for an elliptical crack in an infinite solid subject to arbitrary crack-face traction, can derive the stress intensity factor (SIF) of surface cracks by using the FEA results for an uncracked body. In the present study, the FEAM was applied to evaluations of SIF for noncoplanar multiple surface cracks. The SIF was evaluated for two surface cracks of dissimilar size, and three crack of the same size. The results suggested that the interaction is greatly affected by the relative crack size and negligible when the difference in the crack size is large enough, and the interaction can be evaluated by taking into account the adjacent cracks even if there are many cracks around them. Finally, the crack growth simulations were conducted and a possibility of the direct evaluation of influence of interaction between adjacent crack without using the combination rules was revealed.

Abstract: The finite element alternating method based on the superposition principle has been known as an effective method to obtain the stress intensity factors for general multiple collinear or curvilinear cracks in an isotropic plate. In this paper the method is extended further to solve two-dimensional cracks embedded in a bimaterial plate. The main advantage of this method is that it is not necessary to make crack meshes considering the stress singularity at the crack tip. The solution of the developed code is obtained from an iteration procedure, which alternates independently between the finite element method solution for an uncracked body and the analytical solution for cracks in an infinite body. In order to check the validity of the method, several crack problems of a bimaterial body are solved and compared with the results obtained from the finite element analysis.

Abstract: In order to simulate the growth of arbitrarily shaped three-dimensional cracks, the finite element alternating method is extended. As the required solution for a crack in an infinite body, the symmetric Galerkin boundary element method formulated by Li and Mear is used. In the study, a crack is modeled as distribution of displacement discontinuities, and the governing equation is formulated as singularity-reduced integral equations. With the proposed method several example problems, such as a penny-shaped crack, an elliptical crack in an infinite solid and a semi-elliptical surface crack in an elbow are solved. And their growth under fatigue loading is also considered and the accuracy and efficiency of the method are demonstrated.

Abstract: In order to simulate the growth of arbitrarily shaped three dimensional cracks, the finite element alternating method is extended. As the required analytical solution for a crack in an infinite body, the symmetric Galerkin boundary element method formulated by Li and Mear is used. In the study, a crack is modeled as distribution of displacement discontinuities, and the governing equation is formulated as singularity-reduced integral equations. With the proposed method several example problems for three dimensional cracks in an infinite solid, as well as their growth under fatigue, are solved and the accuracy and efficiency of the method are demonstrated.