Archive of Applied Mechanics

, Volume 84, Issue 2, pp 263–275 | Cite as

A simple method for determining large deflection states of arbitrarily curved planar elastica

Original

Abstract

The paper discusses a relatively simple method for determining large deflection states of arbitrarily curved planar elastica, which is modeled by a finite set of initially straight flexible segments. The basic equations are built using Euler–Bernoulli and large displacement theory. The problem is solved numerically using Runge–Kutta–Fehlberg integration method and Newton method for solving systems of nonlinear equations. This solution technique is tested on several numerical examples. From a comparison of the results obtained and those found in the literature, it can be concluded that the developed method is efficient and gives accurate results. The solution scheme displayed can serve as reference tool to test results obtained via more complex algorithms.

Keywords

Large deflections Arbitrarily curved elastica Geometrical nonlinearity Plane deflection Elastica problem 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Laboratory for Nonlinear Mechanics, Faculty of Mechanical EngineeringUniversity of LjubljanaLjubljanaSlovenia
  2. 2.Department of Mechanical EngineeringMassachusetts Institute of TechnologyCambridgeUSA

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