Acta Mechanica

, Volume 225, Issue 7, pp 1967–1984 | Cite as

A general method for analyzing moderately large deflections of a non-uniform beam: an infinite Bernoulli–Euler–von Kármán beam on a nonlinear elastic foundation

  • T. S. JangEmail author


The present paper concerns a semi-analytical procedure for moderately large deflections of an infinite non-uniform static beam resting on a nonlinear elastic foundation. To construct the procedure, we first derive a nonlinear differential equation of a Bernoulli–Euler–von Kármán “non-uniform” beam on a “nonlinear” elastic foundation, where geometrical nonlinearities due to moderately large deflection and beam non-uniformity are effectively taken into account. The nonlinear differential equation is transformed into an equivalent system of nonlinear integral equations by a canonical representation. Based on the equivalent system, we propose a method for the moderately large deflection analysis as a general approach to an infinite non-uniform beam having a variable flexural rigidity and a variable axial rigidity. The method proposed here is a functional iterative procedure, not only fairly simple but straightforward to apply. Here, a parameter, called a base point of the method, is also newly introduced, which controls its convergence rate. An illustrative example is presented to investigate the validity of the method, which shows that just a few iterations are only demanded for a reasonable solution.


Base Point Nonlinear Differential Equation Elastic Foundation Geometrical Nonlinearity Steady State Error 
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© Springer-Verlag Wien 2014

Authors and Affiliations

  1. 1.Naval Architecture and Ocean EngineeringPusan National UniversityBusanRepublic of Korea

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