Weight optimisation of functionally graded beams using modified differential evolution

Abstract

In this article, an efficient numerical approach for weight optimisation of functionally graded (FG) beams in the presence of frequency constraints is presented. For the analysis purpose, a finite element (FE) solution based on the first order shear deformation theory (FSDT) is established to analyse the free vibration behaviour of FG beams. A four-parameter power law distribution and a five-parameter trigonometric distribution are used to describe the volume fraction of material constituents in the thickness direction. The goal is to tailor the thickness and material distribution for minimising the weight of FG beams while constraining the fundamental frequency to be greater than a prescribed value. The constrained optimisation problem is effectively solved by a novel differential evolution (DE) algorithm. The validity and efficiency of the proposed approach is demonstrated through two numerical examples corresponding to the four-parameter distribution and the five-parameter distribution.
Keywords: FGM beam; lightweight design; frequency constraint; differential evolution.