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A dislocation solution to evaluate the mode III stress intensity factors (SIFs) of the crack tips, torsional rigidity and the hoop stress around the cavities in an infinite rectangular cross-section bar coated by an FG layer under torsion is developed based on the Saint–Venant theory. The solution of the rectangular cross section with the FG coating weakened by a screw dislocation under torsion was first obtained in terms of the dislocation density function. Then, the problem is transformed into a group of Cauchy integral equations in the rectangular cross-section bar with the FG coating layer via the distributed dislocation approach. The singular integral equations are reduced to a set of algebraic equations to evaluate them numerically. After solving the integral equations, the SIFs of the crack tips, the hoop stresses around the cavities and the torsional rigidity of the entire domain are found. The obtained solution is validated by performing comparison studies in multiple cases. It is shown that the interaction between the cracks, the cracks length, variation of the shear module of the FG coating layer and distance of the crack tips from stress-free surfaces can significantly affect the SIFs of crack tips and torsional rigidity of the rectangular cross-section bar coated by an FG layer.

This paper presents the reinforcement impact of a functionally graded (FG) coating layer on the induced stress distribution of circular cross-section bars weakened by multiple cracks and cavities under torsional moment. The entire cross-section of the bar is under torsional loading governed by Saint-Venant’s principle. The shear modulus of the FG coating layer is assumed to vary exponentially in the radial direction. The solution procedure begins by finding the stress field corresponding to a Volterra-type screw dislocation in a circular cross-section bar with an FG coating layer using the Fourier transform. After that, the dislocations are distributed along the surfaces of cracks and cavities. The dislocation stress field is employed to derive singular integral equations in terms of the unknown dislocation density function on the surface of cracks and cavities for the evaluation of multiple defects with arbitrary patterns. These integral equations are of the Cauchy singular kinds and are solved numerically to determine the dislocation density functions on the surface of defects. The obtained results are employed to calculate the torsional rigidity of the domain under consideration, and the mode III stress intensity factors (SIFs) at the crack tips. Finally, several numerical examples are presented to study the effects of the FG coating layer and multiple cracks and cavities with arbitrary patterns on the stress distribution, stress intensity factors (SIFs) and torsional rigidity of weakened bar by cracks and cavities.

This study investigates in to the dynamic response of an inclined cross-ply laminated composite beam traversed by a moving mass. For this purpose, a finite element method based on the classical lamination theory is used. By taking the effects of inertial, Coriolis and centrifugal forces, the property matrices of the moving mass element are extracted. To calculate the overall property matrices of the entire system, we should combine the property matrices of each moving mass element and the overall property matrices for the inclined beam itself. Newmark direct integration method is employed to solve the equation of motion. In order to evidence this study, the numerical results of the isotropic beam are compared to the analytical solution and other numerical results. In addition, the effects of moving mass speed, the Coriolis force, centrifugal force, the frictional force and the inclined angle of beam are studied. Finally, The dynamic response of symmetric cross-ply laminated beam due to moving mass have been compared to the results of an isotropic simple beam.