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The investigation of multiple crack interactions in fracture mechanics is important to predict the safety and reliability of structures. This paper introduces a 2D numerical investigation used to calculate the J-integral of the main crack behavior emanating from a semicircular notch and double semicircular notch and its interaction with another crack which may occur in various positions in titanium /titanium boride functionally graded material (TiB/Ti FGM) plate subjected to tensile mechanical load. Young's modulus of the functionally graded material plate varies along the specimen width (notch radius direction r-FGM) with exponential-law (E-FGM) function. Further, the Poisson's ratio is taken as a constant in normal direction. For this purpose the variations of the material properties are applied at the integration points and at the nodes by implementing a subroutine USDFLD in the ABAQUS software. The variation of the J-integral according to the position, the length, and the angle of rotation of cracks are examined; also the effect of different parameters for double notch FGM plate is investigated as well as the effect of band of FGM within the ceramic plate to reduce Jintegral. According to the numerical analysis, all parameters above played an important role in determining the J-integral.

A refined and simple shear deformation theory for mechanical buckling of composite plate resting on two-parameter Pasternak's foundations is developed. The displacement field is chosen based on assumptions that the in-plane and transverse displacements consist of bending and shear components, and the shear components of in-plane displacements give rise to the parabolic variation of shear strain through the thickness in such a way that shear stresses vanish on the plate surfaces.Therefore, there is no need to use shear correction factor. The number of independent unknowns of present theory is four, as against five in other shear deformation theories.It is assumed that the warping of the cross sections generated by transverse shear is presented by a hyperbolic function. The stability equations are determined using the present theory and based on the existence of material symmetry with respect to the median plane.The nonlinear strain-displacement of Von Karman relations are also taken into consideration. The boundary conditions for the plate are assumed to be simply supported in all edges. Closed-form solutions are presented to calculate the critical load of mechanical buckling, which are useful for engineers in design. The effects of the foundation parameters, side-to-thickness ratio and modulus ratio, the isotropic and orthotropic square plates are presented comprehensively for the mechanical buckling of rectangular composite plates.

This study aims to determine the efficacy of using calcium hydroxide Ca(OH)2 in coagulation process to treat urban liquid effluent from wastewater purification plant. The response surface methodology was used. The effects and interactions between three key process parameters was enhanced applying Box-Behnken design. Factors studied were: coagulant dosage (g/L), coagulation speed (rpm), and coagulation time (min). The treatment efficiency was determined by the turbidity removal rate and the final pH of the treated wastewater. The statistical soundness of the generated model was determined using analysis of variance. The optimal model for determining the relationship between the variables is a second-order quadratic model (R2>98 %). The best turbidity reduction (91.3 %) was obtained using a 0.50 g/L Ca(OH)2 coagulant and 130.1 rpm for 5 minutes. Under these conditions, the ultimate pH of the effluent reached 8.

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