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Application of meshless element free Galerkin method in two-dimensional heat conduction problems

Singh I. V., Sandeep K., Prakash R.

Computer Assisted Mechanics and Engineering Sciences

2004

Vol. 11, No. 4

265-274

In this paper, meshless element free Galerkin method has been used to obtain the numerical solution of transient and steady state heat conduction problems in two-dimensional domains. The unknown function of temperature T(x) has been approximated by moving least square approximant Th(x). These approximants are constructed by using a weight function, a polynomial basis and a set of non-constant coefficients. Variational method is used to obtain the discrete equations. Essential boundary conditions are imposed by Lagrange multiplier technique. Two new weight functions namely hyperbolic and rational have been proposed. The results have been obtained for a two-dimensional model problem using different EFG weight functions and are compared with those obtained by finite element and analytical methods.

Nonlinear dynamic behaviors of high speed rotor supported by rolling element bearings

Harsha S. P., Prakash R., Sandeep K.

International Journal of Applied Mechanics and Engineering

2003

Vol. 8, no 4

705-720

The paper presents a model for investigating structural vibrations in rolling element bearings. The mathematical formulation accounted for tangential motions of rolling elements as well as inner and outer races with the sources of nonlinearity such as the Hertzian contact force, surface waviness and internal radial clearance transition resulting from no contact to contact state between rolling elements and the races. The contacts between the rollers and races are treated as nonlinear springs and the springs act only in compression to simulate the contact deformation and resulting force. The nonlinear stiffness is obtained by using the equations for the Hertzian elastic contact deformation theory. As the nonlinear bearing forces act on the system, a new reduction method and corresponding integration technique is proposed to increase the numerical stability and decrease computer time for system analysis. The effects of various defects of a rotor bearing system in which the rolling element bearings show the periodic, quasi-periodic and chaotic behavior are analyzed. Poincare maps and Fourier spectra are used to elucidate and to illustrate the diversity of the system behavior. It is shown that due to defects such as surface waviness and internal radial clearance the system exhibits an undesirable jump phenomenon with quasi-periodic, subharmonic and chaotic motions.