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In this paper, the anti-plane stress analysis in an infinite elastic plane with multiple cracks is carried out by using the distributed dislocation technique. The solution is obtained for an infinite plane containing the screw dislocation via Fourier transform of biharmonic equation for the analysis of infinite plane in gradient elasticity. These solutions are used to perform integral equations for an infinite plane weakened by multiple straight cracks. Integral equations are hypersingular type which are solved numerically for density of dislocation on the cracks surfaces. The numerical method in Chebyshev series form are used to solve the hypersingular integral equations. The solution of integral equations leads to dislocation density functions. The stress intensity factor for cracks tips are formulated in terms of density of dislocation. Employing the definition of dislocation density, stress intensity factors for cracks tips are calculated. The influence of size-effect and crack location on the stress intensity factors are studied. To confirm the validity of formulations, numerical values of stress intensity factors are compared with the results in the literature. The results of the present approach are in excellent agreement with those in the literature. Some new examples with different geometrics of cracks are solved to illustrate the applicability of procedure.

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Applying and combining h and p refinement techniques in isogeometric method with the possibility of continuity elevation that this method provides, convergence and error of using different kinds of shape functions with different orders and continuities is investigated. It is done in a numerical analysis framework of a practical and well known problem called “Diametral Compression Test”. The advantage of this case is its circular geometry, since IGA provides designers with high potency of the possibility of using minimum elements to make the exact circular geometry. The point load inserts singularity to the problem. The refinement is utilized uniformly as the effective parameters are limited to the kind, order and continuity of shape functions. With different refinement techniques the convergence of approximated solution to the exact solution of linear elasticity is examined. It is concluded that with the singularity that mentioned, the error in IGA is not necessarily reduced with raise in order, more precisely the level of continuity is another important issue to determine error raise. It is also seen that in the presence of point load singularity the rate of error converges to the same value for all degrees of NURBS and lagrangian shape functions with any continuity. At the beginning of refinement process the minimum number of elements is used to make the process clearer to understand. In next steps h and p techniques and their combination is used to refine the model.

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Simulation of the four degree of freedom parallel robot (Quattrotaar) is subjective of this paper. The mathematical model of the parallel robot is obtained too. The workspace is optimized for Non-singular kinematic type-2. Artificial Bees Colony algorithm and Particle Swarm Optimization algorithm as overall exploring algorithms are implemented and the results are compared to each other. Neglect of any intrinsic complexity of the optimization problem the results show the capability of both methods for this robot parameters design. Comparison of the results indicates the Particle Swarm Optimization algorithm runs faster than Artificial Bees Colony algorithm. The exploring volume consists of a plan with 500 mm x 500 mm dimension which moves in a vertical direction from 500 mm to 1000 mm. One of the important hints of the paper is a 90-degree rotation of end effector around vertical axis Z. This rotation is caused more flexibility and dexterity for the robot. A 3-D model of Quattrotaar parallel robot is created by Computer Aided Design software and finally, Quattrotaar is fabricated in Human and Robot Interaction Laboratory (Taarlab)