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Plane Problems (plane + problem)

Distribution by Scientific Domains
Engineering85%

Selected Abstracts

An anisotropic strength criterion for jointed rock masses and its application in wellbore stability analyses

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 6 2008
X. Chen
Abstract In this paper, an anisotropic strength criterion is established for jointed rock masses. An orientation distribution function (ODF) of joint connectivity, is introduced to characterize the anisotropic strength of jointed rock masses related to directional distributed joint sets. Coulomb failure condition is formulated for each plane of jointed rock masses by joint connectivity, where the friction coefficient and cohesion of the jointed rock mass are related to those of the intact rock and joint and become orientation dependent. When approximating joint connectivity by its second-order fabric tensor, an anisotropic strength criterion is derived through an approximate analytical solution to the critical plane problem. To demonstrate the effects of joint distribution on the anisotropic strength of jointed rock masses, the failure envelopes are worked out for different relative orientations of material anisotropy and principal stress axes. The anisotropic strength criterion is also applied to wellbore stability analyses. It is shown that a borehole drilled in the direction of the maximum principal in situ stress is not always the safest due to the anisotropic strength of the jointed rock mass. Copyright © 2007 John Wiley & Sons, Ltd. [source]

Frictional contact of laminated elastic half-spaces allowing interface cavities.

INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2001
Part 1: Analytical treatment
Abstract The paper deals with the plane problem on frictional contact of stratified elastic half-spaces provided discontinuity of their direct touch. Imperfectness of contact of the bodies is assumed to be caused by surface unevenness of their surface layers. The problem is formulated within the framework of the homogenized model with microlocal parameters. Using the method of complex potentials in combination with the method of interface gaps the problem is reduced to a singular integral equation on the function of interface gap height. Copyright © 2001 John Wiley & Sons, Ltd. [source]

Non-stationary plane problem of the successive origination of stress concentrators in a loaded body.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2008
Finite deformations, their superposition
Abstract The first (for the given class of problems) results of solving non-stationary plane problems of non-simultaneous origination of holes and inclusions in a preliminary loaded solid with initial finite strains are presented and discussed. It is taken into account that the origination of a hole or an inclusion produces additional finite deformations (at least, at the vicinity of the hole) superimposed ,physically' on the finite initial ones. The problem is solved using the theory of repeated superposition of large deformations. It is supposed that the shape of stress concentrators is given at the moment of their origination. Calculations were made with the use of the specialized computer package ,Superposition' based on finite-element method. Stress fields are presented at different times. The change of maximal stresses in time is also presented. Copyright © 2008 John Wiley & Sons, Ltd. [source]

On the Ekberg, Kabo and Andersson calculation of the Dang Van high cycle fatigue limit for rolling contact fatigue

FATIGUE & FRACTURE OF ENGINEERING MATERIALS AND STRUCTURES, Issue 6 2004
M. CIAVARELLA
ABSTRACT Recently, various methods have been proposed to assess the risk of rolling contact fatigue failure by Ekberg, Kabo and Andersson, and in particular, the Dang Van multiaxial fatigue criterion has been suggested in a simple approximate formulation. In this note, it is found that the approximation implied can be very significant; the calculation is improved and corrected, and focused on the study of plane problems but for a complete range of possible friction coefficients. It is found that predicted fatigue limit could be much higher than that under standard uniaxial tension/compression for ,hard materials' than for ,ductile materials.' This is in qualitative agreement, for example, with gears' design standards, but in quantitative terms, particularly for frictionless condition, the predicted limit seems possibly too high, indicating the need for careful comparison with experimental results. Some comments are devoted to the interplay of shakedown and fatigue. [source]

Non-stationary plane problem of the successive origination of stress concentrators in a loaded body.

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 12 2008
Finite deformations, their superposition
Abstract The first (for the given class of problems) results of solving non-stationary plane problems of non-simultaneous origination of holes and inclusions in a preliminary loaded solid with initial finite strains are presented and discussed. It is taken into account that the origination of a hole or an inclusion produces additional finite deformations (at least, at the vicinity of the hole) superimposed ,physically' on the finite initial ones. The problem is solved using the theory of repeated superposition of large deformations. It is supposed that the shape of stress concentrators is given at the moment of their origination. Calculations were made with the use of the specialized computer package ,Superposition' based on finite-element method. Stress fields are presented at different times. The change of maximal stresses in time is also presented. Copyright © 2008 John Wiley & Sons, Ltd. [source]

An implicit three-dimensional fully non-hydrostatic model for free-surface flows

INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2004
Hengliang Yuan
Abstract An implicit method is developed for solving the complete three-dimensional (3D) Navier,Stokes equations. The algorithm is based upon a staggered finite difference Crank-Nicholson scheme on a Cartesian grid. A new top-layer pressure treatment and a partial cell bottom treatment are introduced so that the 3D model is fully non-hydrostatic and is free of any hydrostatic assumption. A domain decomposition method is used to segregate the resulting 3D matrix system into a series of two-dimensional vertical plane problems, for each of which a block tri-diagonal system can be directly solved for the unknown horizontal velocity. Numerical tests including linear standing waves, nonlinear sloshing motions, and progressive wave interactions with uneven bottoms are performed. It is found that the model is capable to simulate accurately a range of free-surface flow problems using a very small number of vertical layers (e.g. two,four layers). The developed model is second-order accuracy in time and space and is unconditionally stable; and it can be effectively used to model 3D surface wave motions. Copyright © 2004 John Wiley & Sons, Ltd. [source]

Micromechanically motivated finite element model for ferroelectric ceramics

PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2009
Jayabal K.
Ferroelectric ceramics exhibit significant coupled electromechanical phenomena that have been widely employed in sensor and actuator applications. In regular finite element models dealing with electromechanical plane problems, each grain needs to be subdiscretized by many triangular or quadrilateral elements for required accuracy. This problem can be overcome by a polygonal finite element approach where each grain is modelled by a single finite element without compromising on the results. In this paper, a polygonal finite element approach has been employed to understand the anisotropic response of the ferroelectric ceramics in their piezoelectric region. (© 2009 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]