In this paper, the problem of the circular orthotropic bars with multiple cracks is investigated based on the Saint-Venant torsion theory. The solution to the problem of an orthotropic bar weakened by a Volterra-type screw dislocation is first obtained by means of the finite Fourier sine transform. In this research, the bar is assumed to be subjected to an axial net torsion when finding the dislocation solution. The closed form solution is then derived for displacement and stress fields in the bar. At the next step, the dislocation solution is employed to derive a set of Cauchy singular integral equations for analysis of the circular bar with curved cracks. The solution to these equations is used to determine the torsional rigidity of the bar and the stress intensity factors of the tips of the cracks. The paper is furnished with several examples of a single crack and multiple cracks.

First, using the separation of variables technique a series solution for torsion of an intact finite cylinder under self‐equilibrating lateral shear tractions is given. Next, an integral form solution for torsion of an intact infinite cylinder under the aforementioned lateral loading is obtained. After that the solution of an axisymmetric rotational Somigliana ring dislocation in the infinite circular cylinder is obtained. The distributed dislocation technique is used to construct integral equations for stress analysis of the infinite cylinder with a set of coaxial axisymmetric cracks. These defects are penny‐shaped, annular and circumferential edge cracks. The infinite cylinder is under the action of the loading similar to the intact cylinder. The integral equations are solved numerically to obtain the dislocation density on the surfaces of the cracks. The stress intensity factors for the cracks are determined by employing the dislocation densities. The problem of a cracked finite cylinder is treated by cutting method. That is, a similar cracked infinite cylinder is sliced by extending two additional annular axisymmetric cracks. To validate the cutting method, the solution of the sliced intact infinite cylinder is compared to that of an intact finite cylinder which both of them are under the same self‐equilibrating lateral shear tractions. The solution is applied to several examples to study the effect of crack type/location on the resulting stress intensity factors at tips of the cracks.

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This study presents a formulation for a bar with circular cross-section, coated by a piezoelectric layer and subjected to Saint-Venant torsion loading. The bar is weakened by a Volterra-type screw dislocation. First, with aid of the finite Fourier transform, the stress fields in the circular bar and the piezoelectric layer are obtained. The problem is then reduced to a set of singular integral equations with a Cauchy-type singularity. Unknown dislocation density is achieved by numerical solution of these integral equations. Numerical results are discussed, to reveal the effect of the piezoelectric layer on the reduction of the mechanical stress intensity factor in the bar.

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