In this paper, the analytical solution of an electric and Volterra edge dislocation in a functionally graded piezoelectric (FGP) medium is obtained by means of complex Fourier transform. The system is subjected to inplane mechanical and electrical loading. The material properties of the medium vary exponentially with coordinating parallel to the crack. In this study, the rate of the gradual change of the shear moduli and mass density is assumed to be same. At first, the Volterra edge dislocation solutions are employed to derive singular integral equations in the form of Cauchy singularity for an FGP plane containing Multiple horizontal moving cracks. Then, these equations are solved numerically to obtain dislocation density functions on moving crack surfaces. Finally, the effects of the crack moving velocity, material properties, electromechanical coupling factor and cracks arrangement on the normalized mode I and mode II stress intensity factors and electric displacement intensity factor are studied.

This work deals with the interaction of P-waves between a moving central crack and a pair of outer cracks situated at the interface of an orthotropic layer and an elastic half-space. Initially, we considered a two-dimensional elastic wave equation in orthotropic medium. The Fourier transform has been applied to convert the basic problem to solve the set of four integral equations. These set of integral equations have been solved to get the analytical expressions for the stress intensity factor (SIF) and crack opening displacements (COD) by using the finite Hilbert transform technique and Cooke’ s result. The main objective of this work is to investigate the dynamic stress intensity factors and crack opening displacement at the tips of the cracks. The aims of the study of these physical quantities (SIF, COD) is the prediction of possible arrest of the cracks within a certain range of crack velocity by monitoring applied load. SIF and COD have been depicted graphically for various types of orthotropic materials. We presented a parametric study to explore the influence of crack growing and propagation. This result is very much applicable in bridges, roads, and buildings fractures.

Solvable Graphs (also known as Reachable Graphs) are types of graphs that any arrangement of a specified number of agents located on the graph’s vertices can be reached from any initial arrangement through agents’ moves along the graph’s edges, while avoiding deadlocks (interceptions). In this paper, the properties of Solvable Graphs are investigated, and a new concept in multi agent motion planning, called Minimal Solvable Graphsis introduced. Minimal Solvable Graphs are the smallest graphs among Solvable Graphs in terms of the number of vertices. Also, for the first time, the problem of deciding whether a graph is Solvable form agents is answered, and a new algorithm is presented for making an existing graph solvable and lean for a given number of agents. Finally, through an industrial example, it is demonstrated that how the findings of this paper can be used in designing and reshaping transportation networks (e.g. railways, traffic roads, AGV routs, robotic workspaces, etc.) for Multiple moving agents such as trains, vehicles, and robots.

In this paper, the static problem of several cracks in a functionally graded piezoelectric– piezomagnetic (FGPP) rectangular plane subjected to concentrated anti-plane mechanical and in-plane electric and magnetic fields is described. The material properties are assumed to vary continuously according to exponential functions along the transverse of the FGPP rectangular plane. The dislocation method and integral transforms technique are applied to obtain a set of Cauchy singular integral equations. The field intensity factors for cracks, are obtained by using the corresponding solution to these equations. The numerical examples of mode-III problem are presented to illustrate the interesting mechanical and electromagnetic coupling phenomena induced by multi-crack interactions. Finally, the effects of material non-homogeneity constant, the cracks length and the cracks configuration upon the field intensity factors are investigated. The obtained conclusions seem useful for design of the magneto-electro-elastic structures and devices of high performance.

The solution to the problem of an orthotropic long cylinder subjected to torsional loading is first obtained by means of separation valuables. The cylinder is twisted by two lateral shear tractions, and the ends of the cylinder surface of the cylinder are stress-free. First, the domain under consideration is weakened by an axisymmetric rotational Somigliana ring dislocation. The dislocation solution is employed to derive a set of Cauchy singular integral equations for the analysis of Multiple axisymmetric planner cracks. The numerical solution to these integral equations is used to determine the stress intensity factors for the tips of the concentric planar cracks. A preliminary comparison between results of this study and those available in the literature is performed to confirm the validity of the proposed technique. Several examples of Multiple concentric planner cracks are solved and graphically displayed. Furthermore, the configuration of the cracks and the interaction between cracks is studied.

In this article, stress analysis of an isotropic infinite cylinder weakened by Multiple concentric cylindrical cracks subjected to shear and radial loadings on the lateral surface of the cylinder is accomplished. First, relations for stress and displacement components are given in terms of the Galerkin biharmonic vector potential. Next, using these relations, the dislocation solutions for both Somigliana and Volterra dislocation are derived. Using the distributed dislocation technique, integral equations for the infinite cylinder with arbitrary number of the cylindrical cracks are constructed. The numerical solution of resulting integral equations which are of the Cauchy type singular equations leads to evaluation of Somiglianaand Volterra dislocation densities on the crack surfaces. Using related dislocation densities, the stress intensity factors of crack tips for some examples are attained and variations of them with lengths of cracks are discussed. For some special cases, validation of the results of this study with others available in the literature is done.

Based on the distributed dislocation technique, an analytical solution for the orthotropic layer with functionally graded material (FGM) orthotropic coating containing Multiple axisymmetric interfacial cracks subjected to torsional loading is investigated. It is assumed that the material properties of the FGM orthotropic coating vary power-law form along the thickness of the layer. At first, by using the Hankel transform, the solution for Somigliana-type rotational ring dislocation in the layer and its coating is obtained. Then, the dislocation solution is used to derive a set of singular integral equations for a system of coaxial axisymmetric interface cracks, including penny-shaped and annular cracks. cracks with Cauchy type kernel. The integral equations are of Cauchy singular type, which are solved by Erdogan’, s collocation method for dislocation density on the surface of interfacial crack and the results are used to determine stress intensity factors (SIFs) for axisymmetric interface cracks. Finally, several examples are provided to study the effects of the non-homogeneity constant, orthotropy parameter and thickness of FGM coating on the SIFs for interfacial cracks. The effects of the non-homogeneity constant, orthotropy parameter and thickness of FGM coating as well as the interaction of Multiple interfacial cracks on the SIFs are investigated. The results reveal that the value of the SIFs decreases with increasing the non-homogeneity parameter, orthotropy and thickness of FGM coating. The SIFs for inner tips of annular interface crack are larger than the outer tips.

In uranium yellow cake production, for the extraction and purification of uranium, primarily the uranium ore is grounded, sieved and then leached with (sulphuric acid). The ion-exchange has been identified as a proper method in high perfect recovery of uranium from the acidic solution where uranium concentration is less than 500ppm. This method is operated in two ways: 1 (fixed bed 2) moving bed. moving bed system has some advantages over the fixed bed such as higher mass transfer during ion exchange process. In this study, the effects of various parameters of Multiple compartment ion exchanges in recovery of uranium are investigated. After performing different experiments in batch system, the optimum pH of feed solution was found to be equal to 1.5 and the residence time between the resin and feed solution was 3 hours. Also, the results of fluidized bed continuous system include the optimum flow rate of 22lit/hr and the residence time of 7 minutes (the height of column was 180cm). To increase the efficiency in height limit, the recycle system is used.

In this paper, numerical solutions of Multiple cracks problems in an infinite plate are studied. Hypersingular integral equations (hieq) for the cracks are formulated using the complex potential method. For all kernels such as regular or hypersingular kernels, we are using the appropriate quadrature formulas to solve and evaluate the unknown functions numerically. Furthermore, by using this equation the stress intensity factor (SIF) was calculated for crack tips. For two serial cracks (horizontal) and two dissimilar cracks (horizontal and inclined), our numerical results agree with the previous works.