Multi-domain Formulation Research Articles

Boundary element analysis of gear teeth fracture

The steady state thermoelastic boundary element approach is extended to accommodate mixed-type boundary conditions in two-dimensional domains which may be definite functions of some global variables. This technique is applied to fractured gear teeth in order to evaluate numerically the fracture characterizing parameters. Singular crack elements in conjunction with multidomain formulation are utilized for the computation of mode I and II stress intensity factors. Results are given for some severe crack orientations with respect to crack depth and gear geometry. The present results are very close to those obtained by the finite element method. The influence of heat convection characteristics and mechanical loading conditions are also examined. Stress intensity factors are evaluated for a wide range of operating parameters useful for design purposes.

Coupled magnetoelastic theory of magnetic and magnetostrictive hysteresis

It is demonstrated that hysteresis in the magnetostriction k is coupled to hysteresis in the magnetization M because of the dependence of the magnetostriction on the magnetization. At the same time, when stress is present, the magnetization is in turn coupled to the behavior of the part of the magnetostriction associated with domain moment rotation. An expression for the magnetostriction is formulated, and numerical modeling results for magnetostriction hysteresis are compared to experimental results. Although some features of the magnetostriction in iron and steel still need additional explanation, the main features of the magnetostriction are accounted for. These include liftoff (failure of the magnetostriction to return to its value in the demagnetized state as the hysteresis loop is cycled) and a magnetostriction increase after flux density B reaches its maximum and starts to decrease. A macromagnetic, multidomain formulation that yields zero magnetostriction in the demagnetized specimen is used. >

Three-dimensional stress intensity factor analysis of a surface crack in a high-speed bearing

The boundary element method is applied to calculate the stress intensity factors of a surface crack in the rotating inner raceway of a high-speed roller bearing. The three-dimensional model consists of an axially stressed surface cracked plate subjected to a moving Hertzian contact loading. A multi-domain formulation and singular crack-tip elements were employed to calculate the stress intensity factors accurately and efficiently for a wide range of configuration parameters. The results can provide the basis for crack growth calculations and fatigue life predictions of high performance rolling element bearings that are used in aircraft engines.

Analysis of Crack Propagation in Roller Bearings Using the Boundary Integral Equation Method—A Mixed-Mode Loading Problem

Crack propagation in a rotating inner raceway of a high-speed roller bearing is analyzed using the boundary integral method. The model consists of an edge plate under plane strain condition upon which varying Hertzian stress fields are superimposed. A multidomain boundary integral equation using quadratic elements was written to determine the stress intensity factors KI and KII at the crack tip for various roller positions. The multidomain formulation allows the two faces of the crack to be modeled in two different subregions making it possible to analyze crack closure when the roller is positioned on or close to the crack line. KI and KII stress intensity factors along any direction were computed. These calculations permit determination of crack growth direction along which the average KI times the alternating KI is maximum.