Algorithm for the solution of elastoplastic half-space impact: force-indentation linearisation method

Big-Alabo, A., Harrison, P. and Cartmell, M. P. (2014) Algorithm for the solution of elastoplastic half-space impact: force-indentation linearisation method. Proceedings of the Institution of Mechanical Engineers Part C: Journal of Mechanical Engineering Science, 229(5), pp. 850-858. (doi:10.1177/0954406214541431)

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Abstract

The governing equation of a half-space impact is generally nonlinear and it is normally solved using numerical techniques that are mostly conditionally stable and require many iteration steps for convergence of the solution. In this paper, we present the force-indentation linearisation method (FILM), an approximate technique that produces closed-form solutions of piecewise linearisation of the governing nonlinear differential equation and is capable of producing accurate impact response for an elastoplastic half-space impact. In contrast to the existing numerical techniques, which discretise the impact force or variable of interest in the time-domain, the present technique discretises the impact force with respect to the indentation using successive piecewise linear approximations. Generalised closed-form solutions were derived for each piecewise approximation, and this was used to develop an iterative algorithm for updating the solutions from one piecewise approximation to the next. The results of the present technique matched with results obtained by direct numerical integration of the governing nonlinear differential equation for a half-space impact, and the FILM was found to converge to the results of the numerical solution after a few iterations, typically between five and 10 iterations. The FILM is simple, is inherently stable, converges quickly, gives accurate results and can be implemented manually; these features make it potentially more attractive than the comparable numerical methods.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Cartmell, Prof Matthew and Harrison, Dr Philip
Authors: Big-Alabo, A., Harrison, P., and Cartmell, M. P.
College/School:College of Science and Engineering > School of Engineering > Systems Power and Energy
Journal Name:Proceedings of the Institution of Mechanical Engineers Part C: Journal of Mechanical Engineering Science
Publisher:SAGE Publications
ISSN:0954-4062
ISSN (Online):2041-2983
Copyright Holders:Copyright © 2014 IMechE
First Published:First published in Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 229(5):850-858
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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