An Explicit Solution to Continuum Compliant Cantilever Beam Problem with Various Variational Iteration Algorithms

Abstract

The geometric nonlinearity resulting from large deformation of compliant members has continued to be an interesting research topic in nonlinear mechanics. In this study, two standard variational iteration algorithms, VIM-I and VIM-III are employed to investigate the large deformation of the continuum compliant beam under point load. The VIM is an efficient technique that bypasses the linearization process and proffers solutions to nonlinear problems. The horizontal and vertical displacements of the continuum compliant cantilever beam free end are expressed in explicit analytical forms. Numerical experiment and simulations were carried out to validate the efficacy and applicability of the semi-analytical method. The VIM-I was split into two; VIM-I(A) and VIM-I(B), with the difference being the initial approximations. The results from the VIM-I(A), VIM-I(B) and VIM-III algorithms were compared with the experimental and exact solution. The outcomes reveal that both algorithms correlated well with the analytical solution and experimental result.

Archive of Mechanical Engineering

“…While Ghuku and Saha [28] conducted an experimental and theoretical analysis on the large deflection behaviour of initially curved beams, with different loading. More recently, studies into the nonlinear bending theory of fully nonlinear beams response are still ongoing [29,30] to the investigation into the large deformation of the continuum compliant beam under point load [31].…”