Papers by Keyword: Dynamic Stress Concentration Factor (DSCF)

Abstract: In natural medium, engineering materials and structures, it can be found that there are cavities everywhere. Sometimes the surface of the structure is fixed, and it could be seen as a rigid line. When structure is impacted by dynamic load, the scattering field will be produced because of the cavities and the fixed surface, and it could cause dynamic stress concentration at the edge of the cavities. In this paper, the solution of displacement field for elastic semi-space with fixed surface and multiple cylindrical cavities by anti-plane SH-wave is constructed. In complex plane, considering the displacement boundary condition of the fixed surface, the displacement field aroused by the anti-plane SH-wave and the scattering displacement field impacted by the cylindrical cavities comprised of Fourier-Bessel series with undetermined coefficients are constructed. Through applying the method of multi-polar coordinate system, the equations with unknown coefficients can be obtained by using the stress free condition of the cylindrical cavities in the radial direction. According to orthogonality condition for trigonometric function, these equations can be reduced to a series of algebraic equations. Then the value of the unknown coefficients can be obtained by solving these algebraic equations. The total wave displacement field is the superposition of the displacement field aroused by the anti-plane SH-wave and the scattering displacement field. By using the expressions, an example is provided to show the effect of the change of relative location of the cylindrical cavities. Based on this solution, the problem of interaction of multiple cylindrical cavities and a linear crack in semi-space with fixed surface can be investigated further.

Abstract: The Scattering of SH-wave by a cylindrical elastic inclusion on horizontal interface in bi-material space with a semicircular debonded above subsurface circular cavity have been considered using the methods of complex function and Green function. Firstly, we divide the solution domain along the interface and disconnected boundary into two half-spaces, an upper one and a lower one. And Green function was constructed by using the methods of complex function and multi-polar coordinate. Secondly, the bi-material media was connected along the horizontal interface using the idea of interface conjunction, then undetermined anti-plane forces were loaded at the linking sections respectively to satisfy continuity conditions, and a series of Fredholm integral equations of the first kind to determine that the unknown forces could be set up through continuity conditions on surface. Finally, some examples for DSCF around cylindrical elastic inclusion edge are presented and discussed. Numerical results show that subsurface circular cavitys existence notablely influences DSCF of around cylindrical elastic inclusion edge with a semicircular debonded above subsurface circular cavity.

Abstract: Multiple circular inclusions exists widely in natural media, engineering materials and modern municipal construction. The scattering field produced by multiple circular inclusions determines the dynamic stress concentration factor around the circular inclusions, and therefore determines whether the material is damaged or not. These problems are complicated, because there are many factors influenced. Researchers solved these problems by analysis and numerical methods. It is hard to obtain analytic solutions except for several simple conditions. In this paper, the solution of displacement field for elastic semi-space with multiple cylindrical inclusions by anti-plane SH-wave is constructed. In complex plane, considering the symmetry of SH-wave scattering , the displacement field aroused by the anti-plane SH-wave and the scattering displacement field impacted by the cylindrical inclusions comprised of Fourier-Bessel series with undetermined coefficients which satisfies the stress-free condition on the ground surface are constructed. Through applying the method of multi-polar coordinate system, the equations with unknown coefficients can be obtained by using the displacement and stress condition around the edge of cylindrical inclusions. According to orthogonality condition for trigonometric function, these equations can be reduced to a series of algebraic equations. Then the value of the unknown coefficients can be obtained by solving these algebraic equations. The total wave displacement field is the superposition of the displacement field aroused by the anti-plane SH-wave and the scattering displacement field. By using the expressions, an example is provided to show the effect of the change of relative location of the cylindrical inclusions. Based on this solution, the problem of interaction of multiple cylindrical inclusions and a linear crack in semi-space can be investigated further.

Abstract: Dynamic anti-plane behaviors are studied on two dissimilar piezoelectric media with an interfacial non-circular cavity subjected to time harmonic incident anti-plane shearing. Based on Greens function and conformal mapping method, the dynamic stress concentration factors at the edge of the non-circular cavity are obtained by applying the orthogonal function expansion technique. Numerical cases about two dissimilar piezoelectric media with an elliptic cavity are provided with different elliptic axial length ratio, different wave number and different piezoelectric characteristic parameter. The calculating results show that dynamic analyses are of importance at lower frequencies and larger piezoelectric characteristic parameters.

Abstract: Dynamic antiplane behaviors are investigated theoretically in this paper for a quarter infinite piezoelectric medium with a subsurface circular inclusion. Based on complex variable and mirror image method, the expressions are obtained on dynamic stress concentration factor (DSCF) and electric field intensity concentration factor (EFICF) at the inclusion’s edge caused by the interaction between the inclusion and the right angle edge under time-harmonic anti-plane shearing. While some calculating cases are plotted, so as to show how the frequencies of incident wave, the piezoelectric material’s parameters and the structure’s geometry influence on DSCF and EFICF. The calculating results indicate that dynamic analyses are important to a quarter-infinite piezoelectric medium with defects at the surface vicinity.

Abstract: In mechanical engineering and aerospace engineering, thin plate structure is used widely. For the sake of fixing bolt, it often design open holes in the plate. Sometimes elliptic holes should be used inevitably. When the plate is overloaded or the load is changed regularly, flexural wave is propagating in the plate. Because there are holes, it can cause stress concentration. Stress concentration could decrease the bearing capacity of structure, and reduce the service life of structure. The problem of flexural wave scattering by holes in the plate is one of the important and interesting questions in aerospace engineering for the latest decades. There are lots of materials obtained by theoretical research and experimental investigation. The problem is complicated, because there are many factors influenced. It is hard to obtain analytic solutions except for several simple conditions. In this paper, based on the theory of elastic thin plate, by using wave function expansion method and multi local complex coordinates, scattering of flexural wave and dynamic stress concentration by double elliptic holes in the thin plate are investigated. In the complex plane, the displacement field aroused by incident wave and the scattering displacement field impacted by double elliptic holes comprised of Fourier-Bessel series with undetermined coefficients are constructed. Through applying the method of multi local complex coordinates, the equations with unknown coefficients can be obtained by using the stress-free condition of the double elliptic holes in the radial direction. According to orthogonality condition for trigonometric function, these equations can be reduced to a series of algebraic equations. Then the value of the unknown coefficients can be obtained by solving these algebraic equations. So the analytical solution of this problem is obtained. By using the displacement and stress expressions, an example is provided to show the effect of the change of relative location of the elliptic holes.

Abstract: Based on the scattering theory of elastic waves, employing the wave function expansion method, the scattering and the dynamic stresses concentration of SH wave by circular tunnel with lining are investigated. The analytical solution of the problem is derived, and the numerical solution of the dynamic stress concentration factors around the lining is presented. The effects of the shear elasticity of the surrounding rock and the lining, the wave number on the dynamic stress concentration factors are analyzed. Analysis has shown that the shear elasticity of the surrounding rock and the wave number are factors that influence dynamic stress concentration factor, and provide important theoretical foundation for the earthquake evaluation of lining.

Abstract: In natural medium, engineering materials and structures, it can be found that there are cavities everywhere. When structure is impacted by dynamic load, the scattering field will be produced because of the cavities, and it could cause dynamic stress concentration at the edge of the cavities. In this paper, the solution of displacement field for elastic semi-space with multiple cylindrical cavities by anti-plane SH-wave is constructed. In complex plane, considering the symmetry of SH-wave scattering, the displacement field aroused by the anti-plane SH-wave and the scattering displacement field impacted by the cylindrical cavities comprised of Fourier-Bessel series with undetermined coefficients which satisfies the stress-free condition on the ground surface are constructed. Through applying the method of multi-polar coordinate system, the equations with unknown coefficients can be obtained by using the stress free condition of the cylindrical cavities in the radial direction. According to orthogonality condition for trigonometric function, these equations can be reduced to a series of algebraic equations. Then the value of the unknown coefficients can be obtained by solving these algebraic equations. The total wave displacement field is the superposition of the displacement field aroused by the anti-plane SH-wave and the scattering displacement field. By using the expressions, an example is provided to show the effect of the change of relative location of the cylindrical cavities. Based on this solution, the problem of interaction of multiple cylindrical cavities and a linear crack in semi-space can be investigated further.

Abstract: In mechanical engineering, earthquake engineering and modern municipal construction, semi-cylindrical gap and shallow-buried inclusion structure are used widely. In this paper, Green's Function is studied, which is the solution of displacement field for elastic semi-space with semi-cylindrical gap and multiple shallow-buried inclusions while bearing anti-plane harmonic line source force at any point. In the complex plane, considering the symmetry of SH-wave scattering , the displacement field aroused by the anti-plane harmonic line source force and the scattering displacement field impacted by semi-cylindrical gap and multiple cylindrical inclusions comprised of Fourier-Bessel series with undetermined coefficients which satisfies the stress-free condition on the ground surface are constructed. Through applying the method of multi-polar coordinate system, the equations with unknown coefficients can be obtained by using the displacement and stress condition of the cylindrical inclusion in the radial direction. According to orthogonality condition for trigonometric function, these equations can be reduced to a series of algebraic equations. Then the value of the unknown coefficients can be obtained by solving these algebraic equations. Green's function, that is, the total wave displacement field is the superposition of the displacement field aroused by the anti-plane harmonic line source force and the scattering displacement field. By using the expressions, an example is provided to show the effect of the change of relative location of semi-cylindrical gap , the cylindrical inclusions and the location of the line source force. Based on this solution, the problem of interaction of semi-cylindrical gap , multiple cylindrical inclusions and a linear crack in semi-space can be investigated further.

Abstract: The dynamic response problems of out-plane line loads by a shallow-embedded circular lining structure were investigated here by using the method of Green’s Function. Firstly a suitable Green’s function was constructed, which is an essential solution to the displacement field possessing a shallow-embedded circular lining structure while bearing out-plane harmonic line loads at an arbitrary point. Then we obtained a series of algebraic equations to solve this problem after constructing scattering waves that satisfied the zero-stress condition on the ground surface. Lastly, some numerical examples are given to show the effects that different parameters influence dynamic stress concentration factor (DSCF) by out-plane line source loads.