A generalized elastica-type approach to the analysis of large displacements of spring-strips

An elastica-type analytical solution to the problem of large deflections of slightly curved spring-strips, fixed at one end and loaded at the other with couples and with forces of various directions, is obtained in this work. The main methods of calculation of elliptic integrals are studied, and the limits of their applicability are established as functions of the required degrees of accuracy and of the loading conditions of the spring-strips. The results obtained with the proposed method are then compared to particular cases already developed in the literature with different approaches. It is shown that in all the cases considered the method permits accurate results to be obtained.