A simple and effective solution of the elastica problem

Abstract

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.