Development of Kagome-based functionally graded beams optimized for flexural loadings

Abstract

This study is concerned with the development of an innovative beam geometry based on a tessellation of Kagome unit cells and the improvement of its geometry with the aim of increasing its flexural properties. This aspect was achieved by generating a functionally graded metamaterial structure based on a novel approach that considers the well-established analytical beam theory models as the basis of for the optimization of the structural parameters of the unit cells at an individual level. The starting premise is that the optimal strut thickness variation with the height of the beam will cause the material to yield uniformly in the critical cross-section. Preliminary studies were conducted in order to numerically determine the variation of the stiffness and the strength of the Kagome structure with the thickness of its struts. Considering the equivalent stress distribution during bending in the critical cross-section, an optimal variation of the stiffness with the height of the beam was evaluated. Based on these results, different values for the strut diameter were imposed at corresponding coordinates relative to the neutral axis, assuring a continuous transition across the height of the beam. The flexural properties of the developed functionally graded structure were evaluated using finite element analyses and determined superior characteristics when compared with the data obtained from simulations performed on an uniform Kagome beam with of the same mass. The investigated structures were manufactured through stereolithography and subjected to three-point bending tests, the results being in agreement with the numerical data, thus validating the design.