Analytical solution for a flexural bimodulus beam

Abstract

Formulations for the deformed shape of a simply supported, uniformly loaded bimodulus beam and the location of the neutral axis have been developed. A theoretical model for bimodulus and unimodular beams has been developed to calculate the maximum deflection considering the neutral axis shift in the case of a bimodulus beam. The finite-element technique is used for the evaluation using the concept of the Ambartsumyan bimodular model for simply supported and cantilever bimodulus and unimodular beams with centrally pointed load, uniformly distributed load and gradually varying load. It is found that the value of the maximum deflection is large for a bimodular beam in comparison to that for a unimodular beam for all types of loading. Shifting of neutral axis has been correlated with three point bend testing of graphite specimens. Qualitative comparison for uniformly distributed load and centrally pointed load has been carried out to demonstrate the influence of bimodularity for both cantilever and simply supported numerical specimens based on finite element procedures.