# Cracked semi-infinite cylinder and finite cylinder problems

2006
Kaman, Mete Onur
This work considers a cracked semi-infinite cylinder and a finite cylinder. Material of the cylinder is linearly elastic and isotropic. One end of the cylinder is bonded to a fixed support while the other end is subject to axial tension. Solution for this problem can be obtained from the solution for an infinite cylinder having a penny-shaped rigid inclusion at z = 0 and two penny-shaped cracks at z = ± L. General expressions for this problem are obtained by solving Navier equations using 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 approaches the radius of the cylinder, the ends at z = ± L become cut and subject to uniformly distributed 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.

# Suggestions

 Cracked semi-infinite cylinder and finite cylinder problems Kaman, Mete Onur; Gecit, Mehmet Rusen (Elsevier BV, 2006-12-01) 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 pe...
 Dynamic modeling of spindle-tool assemblies in machining centers Ertürk, Alper; Özgüven, Hasan Nevzat; Department of Mechanical Engineering (2006) Regenerative chatter is a well-known machining problem that results in unstable cutting process, poor surface quality, reduced material removal rate and damage on the machine tool itself. Stability lobe diagrams supply stable depth of cut ا spindle speed combinations and they can be used to avoid chatter. The main requirement for generating the stability lobe diagrams is the system dynamics information at the tool tip in the form of point frequency response function (FRF). In this work, an analytical model ...
 Cracked infinite cylinder with two rigid inclusions under axisymmetric tension Toygar, M. Evren; Gecit, M. Rusen (2006-08-01) This paper considers the problem of an axisymmetric infinite cylinder with a ring shaped crack at z = 0 and two ring-shaped rigid inclusions with negligible thickness at z = +/- L. The cylinder is under the action of uniformly distributed axial tension applied at infinity and its lateral surface is free of traction. It is assumed that the material of the cylinder is linearly elastic and isotropic. Crack surfaces are free and the constant displacements are continuous along the rigid inclusions while the stre...
 Non-linear mathematical modeling of gear rotor bearing systems including bearing clearance Gürkan, Niyazi Ersan; Özgüven, Hasan Nevzat; Department of Mechanical Engineering (2005) In this study, a non-linear mathematical model of gear-rotor systems which consists of elastic shafts on elastic bearings with clearance and coupled by a non-linear gear mesh interface is developed. The mathematical model and the software (NLGRD 2.0) developed in a previous study is extended to include the non-linear effects due to bearing clearances by using non-linear bearing models. The model developed combines the versatility of using finite element method and the rigorous treatment of non-linear effect...
 Fracture mechanical behaviour of visco-elastic materials: application to the so-called dwell-effect NAESER, Bastian; KALISKE, Michael; Dal, Hüsnü; NETZKER, Christiane (Wiley, 2009-08-01) The material force approach is an efficient, elegant, and accepted means to compute the J-integral as a fracture mechanical parameter for elastic and inelastic materials. With the formulation of a multiplicative split of the deformation gradient at hand, rate-dependent (visco-elastic) materials described for example by the physically based Bergstrom-Boyce model can be investigated. For these investigations, the so-called material volume forces have to be computed in order to separate the driving forces acti...
Citation Formats
M. O. Kaman, “Cracked semi-infinite cylinder and finite cylinder problems,” Ph.D. - Doctoral Program, Middle East Technical University, 2006. 