Non-Uniform Leaf Springs with Geometric Nonlinearity

Abstract

The present study deals with the analysis of large deflection of cantilever beams for various cross sections with a transverse load at free end. The aim of this analysis is to study the vertical and horizontal displacement behaviour of leaf springs which is traditionally modeled as cantilever beams of variable cross section. Besides the free end displacement, the variation of stress, strain and the bending moment of the beam are obtained by the technique of minimization of total potential energy principle. The displacement functions are approximated by linear combination of sets of orthogonal coordinate functions, developed through Gram-Schmidt scheme and substituted in the governing equilibrium equation. The final solution of the large displacement geometric nonlinear problem is obtained iteratively with the help of matlab computaional simulation. It is observed that the free end displacements and the maximum stress at fixed end are greatly affected by the geometry of the beam cross section. The present computational method has been validated and some new results have been furnished.