The bending of thin strips with a non-uniform transverse curvature

Abstract

The non-linear flexural behaviour of a tape spring — whose cross section has a uniform curvature — is produced by the presence of an elastic instability. However, these are not the only structures that possess non-linear flexural behaviour. Panel-springs and bridged tape springs are examples of structures that can also produce this behaviour. Predicting the flexural behaviour of these structures is more challenging because their cross section is non-uniform. This work presents an analytical model that can predict the opposite-sense flexural behaviour of thin strips that have a non-uniform cross section. The novel attribute of this model is in the utilisation of a univariate polynomial series to describe the initial cross section of the strip. The model is applied to a range of bridged tape springs and panel-springs, with the results compared with solutions obtained from the Finite Element (FE) method. A consistent error of less than 5.5% is achieved between the analytical model and the FE model when the snap-through moment and propagation moment are compared. The analytical model is also compared with independent experimental data of the flexural behaviour of a traditional carpenter’s tape measure. An error of less than 1% and 7% of the snap-through moment and propagation moment, respectively, is achieved.