Nonlinear Analysis of Leaf Springs of Functionally Graded Materials

Abstract

Abstract The present study deals with the numerical analysis of large deflection of prismatic cantilever beams for various types of material properties with a transverse load at free end, to study the displacement response of leaf springs. Besides the free end displacement, the variation of stress, strain and the bending moment of the beam having variable material properties with the beam length are obtained by the technique of minimization of total potential energy. The mathematical formulation is based on a variational principle using Galerkin's assumed mode method. 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 computational simulation. It is observed that the free end displacements and the shortening of projected beam length are greatly affected by the variation in elasticity modulus value. The present computational method has been validated and some new results have been furnished. The influence of material gradation for various types of exponential and parabolic distribution is shown for three different types of loading.