The existing analytical solutions are extended to obtain the stress fields and the stress intensity factors(SIFs) of two unequal aligned cracks emanating from an elliptical hole in an infinite isotropic plane. A confo...The existing analytical solutions are extended to obtain the stress fields and the stress intensity factors(SIFs) of two unequal aligned cracks emanating from an elliptical hole in an infinite isotropic plane. A conformal mapping is proposed and combined with the complex variable method. Due to some difficulties in the calculation of the stress function, the mapping function is approximated and simplified via the applications of the series expansion. To validate the obtained solution, several examples are analyzed with the proposed method, the finite element method, etc. In addition, the effects of the lengths of the cracks and the ratio of the semi-axes of the elliptical hole(a/b) on the SIFs are studied. The results show that the present analytical solution is applicable to the SIFs for small cracks.展开更多
This paper addresses the problem of plate bending for a doubly connected body with outer and inner boundaries in the form of regular polygons with a common center and parallel sides.The neighborhoods of the vertices o...This paper addresses the problem of plate bending for a doubly connected body with outer and inner boundaries in the form of regular polygons with a common center and parallel sides.The neighborhoods of the vertices of the inner boundary are equal full-strength smooth arcs symmetric about the rays coming from the vertices to the center,but have unknown positions.Rigid bars are attached to the linear parts of the boundary.The plate bends by the moments applied to the middle point bars.The unknown arcs are free from external stresses.The same problem of plate bending is considered for a regular hexagon weakened by a full-strength hole.Using the methods of complex analysis,the analytical image of Kolosov-Muskhelishvili's complex potentials (characterizing an elastic equilibrium of the body),the plate deflection and unknown parts of its boundary are determined under the condition that the tangential normal moment on that plate takes a constant value.Numerical analyses are also performed and the corresponding graphs are constructed.展开更多
A modified polarization saturation model is proposed and addressed math- ematically using a complex variable approach in two-dimensional (2D) semipermeable piezoelectric media. In this model, an existing polarizatio...A modified polarization saturation model is proposed and addressed math- ematically using a complex variable approach in two-dimensional (2D) semipermeable piezoelectric media. In this model, an existing polarization saturation (PS) model in 2D piezoelectric media is modified by considering a linearly varying saturated normal electric displacement load in place of a constant normal electric displacement load, applied on a saturated electric zone. A centre cracked infinite 2D piezoelectric domain subject to an arbitrary poling direction and in-plane electromechanical loadings is considered for the analytical and numerical studies. Here, the problem is mathematically modeled as a non-homogeneous Riemann-Hilbert problem in terms of unknown complex potential functions representing electric displacement and stress components. Having solved the Hilbert problem, the solutions to the saturated zone length, the crack opening displace- ment (COD), the crack opening potential (COP), and the local stress intensity factors (SIFs) are obtained in explicit forms. A numerical study is also presented for the proposed modified model, showing the effects of the saturation condition on the applied electrical loading, the saturation zone length, and the COP. The results of fracture parameters obtained from the proposed model are compared with the existing PS model subject to electrical loading, crack face conditions, and polarization angles.展开更多
文摘The existing analytical solutions are extended to obtain the stress fields and the stress intensity factors(SIFs) of two unequal aligned cracks emanating from an elliptical hole in an infinite isotropic plane. A conformal mapping is proposed and combined with the complex variable method. Due to some difficulties in the calculation of the stress function, the mapping function is approximated and simplified via the applications of the series expansion. To validate the obtained solution, several examples are analyzed with the proposed method, the finite element method, etc. In addition, the effects of the lengths of the cracks and the ratio of the semi-axes of the elliptical hole(a/b) on the SIFs are studied. The results show that the present analytical solution is applicable to the SIFs for small cracks.
文摘This paper addresses the problem of plate bending for a doubly connected body with outer and inner boundaries in the form of regular polygons with a common center and parallel sides.The neighborhoods of the vertices of the inner boundary are equal full-strength smooth arcs symmetric about the rays coming from the vertices to the center,but have unknown positions.Rigid bars are attached to the linear parts of the boundary.The plate bends by the moments applied to the middle point bars.The unknown arcs are free from external stresses.The same problem of plate bending is considered for a regular hexagon weakened by a full-strength hole.Using the methods of complex analysis,the analytical image of Kolosov-Muskhelishvili's complex potentials (characterizing an elastic equilibrium of the body),the plate deflection and unknown parts of its boundary are determined under the condition that the tangential normal moment on that plate takes a constant value.Numerical analyses are also performed and the corresponding graphs are constructed.
文摘A modified polarization saturation model is proposed and addressed math- ematically using a complex variable approach in two-dimensional (2D) semipermeable piezoelectric media. In this model, an existing polarization saturation (PS) model in 2D piezoelectric media is modified by considering a linearly varying saturated normal electric displacement load in place of a constant normal electric displacement load, applied on a saturated electric zone. A centre cracked infinite 2D piezoelectric domain subject to an arbitrary poling direction and in-plane electromechanical loadings is considered for the analytical and numerical studies. Here, the problem is mathematically modeled as a non-homogeneous Riemann-Hilbert problem in terms of unknown complex potential functions representing electric displacement and stress components. Having solved the Hilbert problem, the solutions to the saturated zone length, the crack opening displace- ment (COD), the crack opening potential (COP), and the local stress intensity factors (SIFs) are obtained in explicit forms. A numerical study is also presented for the proposed modified model, showing the effects of the saturation condition on the applied electrical loading, the saturation zone length, and the COP. The results of fracture parameters obtained from the proposed model are compared with the existing PS model subject to electrical loading, crack face conditions, and polarization angles.