A simple and effective solution of the elastica problem

The bending behaviour of thin stripes and leaf springs, in the presence of large deflections, is ruled by the so-called Bernoulli—Euler equation. The standard solution approach of this problem (‘elastica’) is represented by the non-linear finite-element analysis. In some special cases, closed-form s...

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Bibliographic Details
Published in:Proceedings of the Institution of Mechanical Engineers. Part C, Journal of mechanical engineering science Journal of mechanical engineering science, 2008-12, Vol.222 (12), p.2513-2516
Main Authors: Campanile, L F, Hasse, A
Format: Article
Language:English
Subjects:
Circularity
Deformation
Design analysis
Design optimization
Discretization
Economic models
Elliptic functions
Euler-Bernoulli equation
Exact solutions
Finite element analysis
Finite element method
Integrals
Kinematics
Leaf springs
Materials elasticity
Mathematical analysis
Mechanical engineering
Modulus of elasticity
Nonlinearity
Segments
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Summary:The bending behaviour of thin stripes and leaf springs, in the presence of large deflections, is ruled by the so-called Bernoulli—Euler equation. The standard solution approach of this problem (‘elastica’) is represented by the non-linear finite-element analysis. In some special cases, closed-form solutions are available, which involve elliptic integrals and functions. In this article, an alternative method is presented based on the discretization of the deformed beam into circular-arc segments. The method is fast and simple to implement, and therefore suits well for the design and optimization of compliant kinematics.
ISSN:0954-4062
2041-2983
DOI:10.1243/09544062JMES1244