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R.t. Faal - One of the best experts on this subject based on the ideXlab platform.

  • Saint-Venant torsion analysis of bars with rectangular cross-section and effective coating layers
    Applied Mathematics and Mechanics-english Edition, 2016
    Co-Authors: H. Teimoori, R.t. Faal, Raj Das
    Abstract:

    This paper investigates the torsion analysis of coated bars with a rectangular cross-section. Two opposite faces of a bar are coated by two isotropic layers with different materials of the original substrate that are perfectly bonded to the bar. With the Saint-Venant torsion theory, the governing equation of the problem in terms of the warping function is established and solved using the finite Fourier Cosine Transform. The state of stress on the cross-section, warping of the cross-section, and torsional rigidity of the bar are evaluated. Effects of thickness of the coating layers and material properties on these quantities are investigated. A set of graphs are provided that can be used to determine the coating thicknesses and material properties so as to keep the maximum von Mises stress on the cross-section below an allowable value for effective use of the coating layer.

  • Saint-Venant torsion of orthotropic bars with rectangular cross section weakened by cracks
    International Journal of Solids and Structures, 2015
    Co-Authors: Alireza Hassani, R.t. Faal
    Abstract:

    Abstract The solution to problem of a Volterra-type screw dislocation in an orthotropic bar with rectangular cross section is first obtained by means of a finite Fourier Cosine Transform. The bar is under axial torque which is governed by the Saint-Venant torsion theory. The series solution is then derived for displacement and stress fields in the bar cross section. The dislocation solution is employed to derive a set of Cauchy singular integral equations for the analysis of curved cracks. The solution to these equations is used to determine the torsional rigidity of bar and the stress intensity factors (SIFs) for the tips of the cracks. Several examples of a single straight crack and an arc-crack are solved. Furthermore, the interaction between two cracks is studied. Finally, the stress components around an inclined edge crack tip are used to define the boundary of the plastic region employing von Mises yield criterion.

  • Anti-plane stress analysis of dissimilar sectors with multiple defects
    Applied Mathematical Modelling, 2013
    Co-Authors: R.t. Faal, Alireza Pasrad, A.s. Milani
    Abstract:

    AbstractIn this article, the anti-plane deformation of a typical dissimilar sector consists of two sub-sectors attached to each other on one circular edge is studied. The solution of a Volterra type screw dislocation problem in the sector is obtained through finite Fourier Cosine Transform. Exact closed-form solutions for the displacement and stress fields are also presented. Next, using a distributed dislocation method, integral equations of the sectors weakened by cracks and cavities under an anti-plane traction are obtained. The defects are assumed to be located only in one of the sub-sector regions. The obtained equations for the latter problem are of the Cauchy singular type and have been solved numerically. Several examples are presented to demonstrate the efficiency and applicability of the proposed solution procedure. The geometric and force singularities of the stress field are studied and compared to those reported in the literature

  • Stress analysis of two kinds of dissimilar isotropic sectors
    Mathematics and Mechanics of Solids, 2012
    Co-Authors: R.t. Faal, Alireza Pasrad
    Abstract:

    Anti-plane stress analysis of two different kinds of dissimilar sectors has been accomplished in our study. The first kind of dissimilar sectors consists of two isotropic sectors perfectly attached to each other along their circular edges. In the second kind, these isotropic sectors are joined perfectly in the radial interface. Solutions to the differential equations governing the dissimilar sector are found by utilizing finite Fourier Cosine Transform as well as the technique of the separation of variables. The closed-form solutions are obtained for the displacement and stress fields in each sector. Also the geometric and force singularities of the stress fields are studied and compared with those in the past research. In the special case, i.e. finite wedges, the results for the stress fields are in complete agreement with those in the literature.

  • Stress analysis of the cracked and uncracked transversely isotropic sectors with different types of boundary conditions
    Mathematics and Mechanics of Solids, 2012
    Co-Authors: R.t. Faal, Alireza Hassani
    Abstract:

    The anti-plane deformation of an uncracked transversely isotropic sector is studied for two different types of boundary conditions. The solution of the problem is accomplished by means of two methods for each boundary condition, namely using the finite Fourier Cosine Transform and the method of separation of variables. The closed-form solutions are obtained for displacement and stress fields in the whole domain for each kind of boundary conditions. In the special cases, i.e. finite wedges, the results for the stress field show an exact agreement with those in the literature. In the following, the stress analysis of a transversely isotropic sectors weakened by a circular crack as well as radial crack is accomplished. The resultant singular integral equation of the Cauchy type are solved numerically and, finally, the stress intensity factors of the crack tips versus the ratios of the material properties are plotted and discussed.

Alireza Hassani - One of the best experts on this subject based on the ideXlab platform.

  • Analytical Stress Solutions of an Orthotropic Sector Weakened by Multiple Defects by Dislocation Approach
    Journal of Solid Mechanics, 2020
    Co-Authors: A.r Hassani, Alireza Hassani
    Abstract:

    In this article, the anti-plane deformation of an orthotropic sector with multiple defects is studied analytically. The solution of a Volterra-type screw dislocation problem in a sector is first obtained by means of a finite Fourier Cosine Transform. The closed form solution is then derived for displacement and stress fields over the sector domain. Next, the distributed dislocation method is employed to obtain integral equations of the sector with cracks and cavities under anti-plane traction. These equations are of Cauchy singular kind, which are solved numerically by generalizing a numerical method available in the literature by means of expanding the continuous integrands of integral equations with different weight functions in terms of Chebyshoff and Jacobi polynomials. A set of examples are presented to demonstrate the applicability of the proposed solution procedure. The geometric and force singularities of stress fields in the sector are also studied and compared to the earlier reports in the literature.

  • Analysis of cracked bars with rectangular cross-section and isotropic coating layer under torsion
    International Journal of Mechanical Sciences, 2017
    Co-Authors: Alireza Hassani, M.m. Monfared
    Abstract:

    Abstract The solution to problem of a Volterra-type screw dislocation in a rectangular cross section bar with an isotropic coating is first achieved by means of a finite Fourier Cosine Transform. The bar is under axial torque which is governed by Saint-Venant torsion theory. The series solution is then derived for warping function and stress fields in the rectangular cross section with an isotropic coating. The dislocation solution is employed to derive a set of Cauchy singular integral equations for the analysis of smooth cracks. The solution of these equations is used to determine the torsional rigidity of bar and the stress intensity factors for the crack tips. Finally, several examples are presented to show the accuracy and efficiency of the dislocation technique in Saint-Venant torsion problems.

  • Saint-Venant torsion of orthotropic bars with rectangular cross section weakened by cracks
    International Journal of Solids and Structures, 2015
    Co-Authors: Alireza Hassani, R.t. Faal
    Abstract:

    Abstract The solution to problem of a Volterra-type screw dislocation in an orthotropic bar with rectangular cross section is first obtained by means of a finite Fourier Cosine Transform. The bar is under axial torque which is governed by the Saint-Venant torsion theory. The series solution is then derived for displacement and stress fields in the bar cross section. The dislocation solution is employed to derive a set of Cauchy singular integral equations for the analysis of curved cracks. The solution to these equations is used to determine the torsional rigidity of bar and the stress intensity factors (SIFs) for the tips of the cracks. Several examples of a single straight crack and an arc-crack are solved. Furthermore, the interaction between two cracks is studied. Finally, the stress components around an inclined edge crack tip are used to define the boundary of the plastic region employing von Mises yield criterion.

  • Stress analysis of the cracked and uncracked transversely isotropic sectors with different types of boundary conditions
    Mathematics and Mechanics of Solids, 2012
    Co-Authors: R.t. Faal, Alireza Hassani
    Abstract:

    The anti-plane deformation of an uncracked transversely isotropic sector is studied for two different types of boundary conditions. The solution of the problem is accomplished by means of two methods for each boundary condition, namely using the finite Fourier Cosine Transform and the method of separation of variables. The closed-form solutions are obtained for displacement and stress fields in the whole domain for each kind of boundary conditions. In the special cases, i.e. finite wedges, the results for the stress field show an exact agreement with those in the literature. In the following, the stress analysis of a transversely isotropic sectors weakened by a circular crack as well as radial crack is accomplished. The resultant singular integral equation of the Cauchy type are solved numerically and, finally, the stress intensity factors of the crack tips versus the ratios of the material properties are plotted and discussed.

  • Stress analysis of transversely isotropic sectors weakened by multiple defects
    International Journal of Solids and Structures, 2012
    Co-Authors: R.t. Faal, Alireza Hassani, A.s. Milani
    Abstract:

    In this article, the anti-plane deformation of a transversely isotropic sector with multiple defects is studied analytically. The solution of a Volterra-type screw dislocation problem in a sector is first obtained by means of a finite Fourier Cosine Transform. The closed form solution is then derived for displacement and stress fields over the sector domain. Next, the distributed dislocation method is employed to obtain integral equations of the sector with cracks and cavities under an anti-plane traction. The ensuing integral equations are of the Cauchy type singular and have been solved numerically. A set of examples are presented to demonstrate the applicability of the proposed solution procedure. The geometric and force singularities of stress fields in the sector are also studied and compared to the earlier reports in the literature.

A.s. Milani - One of the best experts on this subject based on the ideXlab platform.

  • Anti-plane stress analysis of dissimilar sectors with multiple defects
    Applied Mathematical Modelling, 2013
    Co-Authors: R.t. Faal, Alireza Pasrad, A.s. Milani
    Abstract:

    AbstractIn this article, the anti-plane deformation of a typical dissimilar sector consists of two sub-sectors attached to each other on one circular edge is studied. The solution of a Volterra type screw dislocation problem in the sector is obtained through finite Fourier Cosine Transform. Exact closed-form solutions for the displacement and stress fields are also presented. Next, using a distributed dislocation method, integral equations of the sectors weakened by cracks and cavities under an anti-plane traction are obtained. The defects are assumed to be located only in one of the sub-sector regions. The obtained equations for the latter problem are of the Cauchy singular type and have been solved numerically. Several examples are presented to demonstrate the efficiency and applicability of the proposed solution procedure. The geometric and force singularities of the stress field are studied and compared to those reported in the literature

  • Stress analysis of transversely isotropic sectors weakened by multiple defects
    International Journal of Solids and Structures, 2012
    Co-Authors: R.t. Faal, Alireza Hassani, A.s. Milani
    Abstract:

    In this article, the anti-plane deformation of a transversely isotropic sector with multiple defects is studied analytically. The solution of a Volterra-type screw dislocation problem in a sector is first obtained by means of a finite Fourier Cosine Transform. The closed form solution is then derived for displacement and stress fields over the sector domain. Next, the distributed dislocation method is employed to obtain integral equations of the sector with cracks and cavities under an anti-plane traction. The ensuing integral equations are of the Cauchy type singular and have been solved numerically. A set of examples are presented to demonstrate the applicability of the proposed solution procedure. The geometric and force singularities of stress fields in the sector are also studied and compared to the earlier reports in the literature.

Ch. Zhang - One of the best experts on this subject based on the ideXlab platform.

  • Anti-plane shear Green's functions for an isotropic elastic half-space with a material surface
    International Journal of Solids and Structures, 2010
    Co-Authors: Weiqiu Chen, Ch. Zhang
    Abstract:

    Abstract This paper presents analytical Green’s function solutions for an isotropic elastic half-space subject to anti-plane shear deformation. The boundary of the half-space is modeled as a material surface, for which the Gurtin–Murdoch theory for surface elasticity is employed. By using Fourier Cosine Transform, analytical solutions for a point force applied both in the interior or on the boundary of the half-space are derived in terms of two particular integrals. Through simple numerical examples, it is shown that the surface elasticity has an important influence on the elastic field in the half-space. The present Green’s functions can be used in boundary element method analysis of more complicated problems.

  • Anti-plane shear Green’s functions for an isotropic elastic half-space with a material surface
    International Journal of Solids and Structures, 2010
    Co-Authors: W.q. Chen, Ch. Zhang
    Abstract:

    AbstractThis paper presents analytical Green’s function solutions for an isotropic elastic half-space subject to anti-plane shear deformation. The boundary of the half-space is modeled as a material surface, for which the Gurtin–Murdoch theory for surface elasticity is employed. By using Fourier Cosine Transform, analytical solutions for a point force applied both in the interior or on the boundary of the half-space are derived in terms of two particular integrals. Through simple numerical examples, it is shown that the surface elasticity has an important influence on the elastic field in the half-space. The present Green’s functions can be used in boundary element method analysis of more complicated problems

Zhangxin Chen - One of the best experts on this subject based on the ideXlab platform.

  • semi analytical solution for pressure transient analysis of a hydraulically fractured vertical well in a bounded dual porosity reservoir
    Journal of Hydrology, 2018
    Co-Authors: Morteza Dejam, Hassan Hassanzadeh, Zhangxin Chen
    Abstract:

    Abstract We study the role of a hydraulic fracture on the pressure transient behavior of a vertical well producing from a bounded (or finite) dual-porosity formation. A combination of Laplace Transform (LT) and the finite Fourier Cosine Transform (FFCT) are used to solve the diffusivity equation. The presented analysis allows identification of five flow regimes, including: 1) early linear flow, 2) volumetric depletion of natural fractures, 3) natural-fracture radial flow, 4) transition from natural-fracture radial flow to total (natural fractures and matrix) radial flow, and 5) pseudo-steady state flow. The results reveal that the interporosity flow coefficient, storativity ratio, natural-fracture permeability anisotropy, and reservoir size play significant roles on the identified flow regimes compared to the hydraulically fractured well location and reservoir shape. The developed solution can be useful for well test analysis by generating a new set of type curves or can be applicable to a forward model for estimating parameters of reservoir. This study presents a new semi-analytical solution which finds application in well testing of hydraulically fractured wells in dual-porosity formations.