Open Access

ARTICLE

Finite Deflection of Slender Cantilever with Predefined Load Application Locus using an Incremental Formulation

by D. P,it¹, N. Thomas², Bhakti Patel¹, S.M. Srinivasan¹

1 IIT, Madras, Chennai, India
2 Texas A & M University, College Station, Texas, USA.

Computers, Materials & Continua 2015, 45(2), 127-144. https://doi.org/10.3970/cmc.2015.045.127

Abstract

In this paper, a class of problems involving space constrained loading on thin beams with large deflections is considered. The loading is such that, the locus of the force application point moves along an arbitrarily predefined path, fixed in space. Both linear elastic as well as elastic-perfectly plastic materials are considered. A simplification is realized using the moment-curvature relationship directly. The governing equation obtained is highly non-linear owing to inclusion of both material and geometric non-linearity. A general algorithm is described to solve the governing equation using an incremental formulation coupled with Runge Kutta 4^th order initial value explicit solver. Additionally, the presented method is capable of handling unloading and reverse loading conditions. An example problem where the load application point locus is an inclined straight line is solved to demonstrate the performance of the method. It is found that, the force response due to the inclined locus is stiffer than the vertical locus. This response is akin to dry friction condition on a vertical locus case.

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Keywords

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