A semi-analytical simulation method for bi-directional functionally graded cantilever beams under arbitrary static loads

Abstract

This paper presents a novel semi-analytical simulation approach for analysing the behaviour of bi-directional functionally graded cantilever beams subjected to arbitrary static loads, such as concentrated moments, concentrated forces, distributed force and their combinations applied at any location along the beam. The fundamental equations governing the cantilever beam’s response are derived, on the basis of which the proposed semi-analytical method is implemented using MATLAB programming language. The simulation results include field variables as well as stress contours, providing a compressive understanding of the beam’s behaviour. To validate the accuracy and reliability of the proposed method, a convergence study is conducted in comparison with the graded finite element method (GFEM) and analytical solutions. In the end, the developed method is applied to simulate the bending behaviour of bi-directional functionally graded cantilever beams under various loads individually and their combinations. The stress contours and deflection curves obtained from the simulation are compared with the solutions obtained using GFEM, revealing that the developed method possesses excellent capability in accurately simulating the bending behaviour of cantilever beams.