Cylindrical Co-ordinate System (cylindrical + co-ordinate_system)

Distribution by Scientific Domains


Selected Abstracts


The Reissner,Sagoci problem for a transversely isotropic half-space

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2006
Mohammad Rahimian
Abstract A transversely isotropic linear elastic half-space, z,0, with the isotropy axis parallel to the z -axis is considered. The purpose of the paper is to determine displacements and stresses fields in the interior of the half-space when a rigid circular disk of radius a completely bonded to the surface of the half-space is rotated through a constant angle ,0. The region of the surface lying out with the circle r,a, is free from stresses. This problem is a type of Reissner,Sagoci mixed boundary value problems. Using cylindrical co-ordinate system and applying Hankel integral transform in the radial direction, the problem may be changed to a system of dual integral equations. The solution of the dual integral equations is obtained by an approach analogous to Sneddon's (J. Appl. Phys. 1947; 18:130,132), so that the circumferential displacement and stress fields inside the medium are obtained analytically. The same problem has already been approached by Hanson and Puja (J. Appl. Mech. 1997; 64:692,694) by the use of integrating the point force potential functions. It is analytically proved that the present solution, although of a quite different form, is equivalent to that given by Hanson and Puja. To illustrate the solution, a few plots are provided. The displacements and the stresses in a soil deposit due to a rotationally symmetric force or boundary displacement may be obtained using the results of this paper. Copyright © 2006 John Wiley & Sons, Ltd. [source]


Semi-analytical far field model for three-dimensional finite-element analysis

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2004
James P. Doherty
Abstract A challenging computational problem arises when a discrete structure (e.g. foundation) interacts with an unbounded medium (e.g. deep soil deposit), particularly if general loading conditions and non-linear material behaviour is assumed. In this paper, a novel method for dealing with such a problem is formulated by combining conventional three-dimensional finite-elements with the recently developed scaled boundary finite-element method. The scaled boundary finite-element method is a semi-analytical technique based on finite-elements that obtains a symmetric stiffness matrix with respect to degrees of freedom on a discretized boundary. The method is particularly well suited to modelling unbounded domains as analytical solutions are found in a radial co-ordinate direction, but, unlike the boundary-element method, no complex fundamental solution is required. A technique for coupling the stiffness matrix of bounded three-dimensional finite-element domain with the stiffness matrix of the unbounded scaled boundary finite-element domain, which uses a Fourier series to model the variation of displacement in the circumferential direction of the cylindrical co-ordinate system, is described. The accuracy and computational efficiency of the new formulation is demonstrated through the linear elastic analysis of rigid circular and square footings. Copyright © 2004 John Wiley & Sons, Ltd. [source]


Scaled boundary finite-element analysis of a non-homogeneous axisymmetric domain subjected to general loading

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 10 2003
James P. Doherty
Abstract The scaled boundary finite-element method is derived for elastostatic problems involving an axisymmetric domain subjected to a general load, using a Fourier series to model the variation of displacement in the circumferential direction of the cylindrical co-ordinate system. The method is particularly well suited to modelling unbounded problems, and the formulation allows a power-law variation of Young's modulus with depth. The efficiency and accuracy of the method is demonstrated through a study showing the convergence of the computed solutions to analytical solutions for the vertical, horizontal, moment and torsion loading of a rigid circular footing on the surface of a homogeneous elastic half-space. Computed solutions for the vertical and moment loading of a smooth rigid circular footing on a non-homogeneous half-space are compared to analytical ones, demonstrating the method's ability to accurately model a variation of Young's modulus with depth. Copyright © 2003 John Wiley & Sons, Ltd. [source]


Study of non-Fickian diffusion problems with the potential field in the cylindrical co-ordinate system

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2003
Han-Taw Chen
Abstract The present study applies a hybrid numerical scheme of the Laplace transform technique and the control volume method in conjunction with the hyperbolic shape functions to investigate the effect of a potential field on the one-dimensional non-Fickian diffusion problems in the cylindrical co-ordinate system. The Laplace transform method is used to remove the time-dependent terms in the governing differential equation and the boundary conditions, and then the resulting equations are discretized by the control volume scheme. The primary difficulty in dealing with the present problem is the suppression of numerical oscillations in the vicinity of sharp discontinuities. Results show that the present numerical results do not exhibit numerical oscillations and the potential field plays an important role in the present problem. The strength of the jump discontinuity can be reduced by increasing the value of the potential gradient. The propagation speed of mass wave is independent of the potential gradient and the boundary condition. Copyright © 2003 John Wiley & Sons, Ltd. [source]


Analysis of heat transfer characteristics of an unsaturated soil bed: a simplified numerical method

INTERNATIONAL JOURNAL OF ENERGY RESEARCH, Issue 15 2001
Gopal B. Reddy
Abstract This paper is a continuation of a study reported in this Journal in February 1999. The paper presents a summary of the two-dimensional macroscopic continuity, momentum and energy equations in a cylindrical co-ordinate system that describe heat and mass transfer through unsaturated soil. The hydrodynamic laws governing flow of water through unsaturated soil are also presented. The explicit numerical procedure and the method to solve the equations are described. Characteristics of the corresponding computer program are also discussed. The results obtained with the current cylindrical governing equations are compared with the previously reported results based upon the Cartesian system of equations. It is observed that the results obtained with cylindrical formulations are in closer agreement with the experimental results. The effects of various heat transfer processes as well as the motion of fluids on heat transfer in a clay bed coupled to a heat pump are discussed. Heat diffusion into the soil by conduction is shown to be predominant through the early stage of heating, while the liquid water motion contributes to heat transfer during the intermediate times and the gas motion is shown to become significant during the last stages of drying. The contribution of the convective transport increases with the temperature and becomes equal to the contribution by conduction at moderately high temperatures. Copyright © 2001 John Wiley & Sons, Ltd. [source]