In this paper, the plates made of functionally graded material (FGM) with and without a crack are numerically simulated, employing the finite element method (FEM). The material property variations are defined to be fully continuous; therefore, the elements can be as small as required. For this purpose, variations of the material properties are applied in both the integration points and in the n...

Fracture assessment of U- and V-notches is important in mechanical engineering. One can use the J-integral as fracture parameter in order to predict the critical fracture load in notches. The critical value of the J-integral in cracks is a function of the material properties. In notches, however, the material properties as well as the notch dimensions affect this critical value (named fracture ...

Contemporary research has proved that Mittag-Leffler function is the solution of fractional differential and integral equations. Fractional Calculus is rapidly gaining recognition as an important branch of Mathematical Sciences. In this paper, we study a newly defined Mittag-Leffler type E-function that unifies many special functions including some newly defined generalized trigonometric functi...

In this paper, the influence of notch depth-to-width ratios on J-integral and critical load of Aluminium 8011 alloy specimens with U-notch under Mode I loading are studied. Using experiments, for a set of specimens having different notch depth–to–width ratios, J-integral was found and the same was verified using analytical methods. Further, using the results obtained from the experiments, failu...

The elastic-plastic behavior of the material is considered to analyze the effect of an external circumferential crack on a pipe with thickness transition and double slopes. Using the extended finite element method (XFEM), the J-integral of 3D cracks were investigated and compared between straight pipes and pipes with thickness transition and different slopes. Considering internal press...

The aim of this paper is to study some properties of multiindex Mittag-Leffler type function E(1/ρj),(μj)(z) introduced by Kiryakova [V. Kiryakova, J. Comput. Appl. Math. 118 (2000), 241-259]. Here we establish certain theorems which provide the image of this function under the Saigo’s fractional integral operators. The results derived are of general character and give rise to a number of known...

using qcd factorization for the hadronic matrix elements, we show that existing data, inparticular the branching ratios br ( b →j/ψk) and br ( b →j/ψπ), can be accounted for in this approach.we analyze the decay b j /k( ) within the framework of qcd factorization. the calculation of therelevant hard-scattering kernels for twist-2 and twist-3 is completed. we calculate this decay in a special...

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 discontinu...