Cracked semi-infinite cylinder and finite cylinder problems

This work considers the analysis of a cracked semi-infinite cylinder and a finite cylinder. Material of the cylinder is assumed to be linearly elastic and isotropic. One end of the cylinder is bonded to a fixed support while the other end is subjected to axial tension. Solution of this problem can be obtained by superposition of solutions for an infinite cylinder subjected to uniformly distributed tensile load at infinity (I) and an infinite cylinder having a penny-shaped rigid inclusion at z = 0 and two penny-shaped cracks at z = L (II). General expressions for the perturbation problem (II) are obtained by solving Navier equations with Fourier and Hankel transforms. When the radius of the inclusion approaches the radius of the cylinder, the end at z = 0 becomes fixed and when the radius of the cracks approach the radius of the cylinder, the ends at Z = +/- L become cut and subject to uniform tensile load. Formulation of the problem is reduced to a system of three singular integral equations. By using Gauss-Lobatto and Gauss-Jacobi integration formulas, these three singular integral equations are converted to a system of linear algebraic equations which is solved numerically. (c) 2006 Published by Elsevier Ltd

Axisymmetric finite cylinder with one end clamped and the other under uniform tension containing a penny-shaped crack

This study considers the axisymmetric analysis of a finite cylinder containing a penny-shaped transverse crack. Material of the cylinder is assumed to be linearly elastic and isotropic. One end of the cylinder is bonded to a fixed support while the other end is subjected to uniform axial tension. Solution is obtained by superposing the solutions for an infinite cylinder loaded at infinity and an infinite cylinder containing four cracks and a rigid inclusion loaded along the cracks and the inclusion. When the radius of the inclusion approaches the radius of the cylinder, its mid-plane becomes fixed and when the radius of the distant cracks approach the radius of the cylinder, the ends become cut and subject to uniform tensile loads. General expressions for the perturbation problem are obtained by solving Navier equations with Fourier and Hankel transforms. Formulation of the problem is reduced to a system of five singular integral equations. By using Gauss-Lobatto and Gauss-Jacobi integration formulas, these five singular integral equations are converted to a system of linear algebraic equations which is solved numerically. Stress distributions along the rigid support, stress intensity factors at the edges of the rigid support and the crack are calculated

Biomechanical and histological outcome of combined raloxifene-estrogen therapy on skeletal and reproductive tissues

Estrogen replacement is a potent therapy for postmenopausal osteoporosis. However, its carcinogenic effects on breasts and the uterus limit its utilization. Raloxifene has estrogen-like effects on bones without the carcinogenic symptoms on breast or uterine tissue. Their individual effects are well characterized, but the results of their interaction remains elusive. In this work, we investigate the consequences of a combined raloxifene/estrogen therapy on bone and uterus with experimental osteoporosis. 40 Wistar rats began treatment 3 months post-ovariectomy. Estrogen and raloxifene were administered 0.03 mg/kg/day and 1.5 mg/kg/day separately and together for 5 times per week for 12 weeks. Biomechanical tests and bone mineral density measurements, histology of uterus, and blood markers were analyzed. The co-administration group had higher toughness and ultimate strength than the ovariectomized controls (P<0.01). E+R had better biomechanical properties than the single treatments; yet the differences were not significant. Uterus histology signified high degeneration in the estrogen group. The raloxifene group had less degeneration but higher vascularization. Less immune reaction and vascularization were observed in the group with combined dosage than in those with individual treatments. Hence, the uterus of the combined treatment had fewer side effects than the ones that were individually treated. Mutual antagonization might be possible between raloxifene and estrogen, and that might have caused a decrease in the adverse effects. Overall, combined therapy might be useful to minimize the individual side effects of raloxifene and estrogen on the uterus and still provide bone strength and toughness