Mathematical design and preliminary mechanical analysis of the new lattice structure: “GE-SEZ*” structure processed by ABS polymer and FDM technology

Abstract

In this study, the authors propose a new design of a novel class of lattice structures. The new design is based on two main geometrical properties, the “volume” and the “surface to volume ratio”. It takes advantage of the strongest column designed against buckling proposed by Keller (Arch Ration Mech Anal 5:275–285, 1960) and Seiranyan (J Appl Math Mech 51(2):272–275, 1987). The Schoen minimal gyroid is used as a reference to establish the necessary lightweight property of the proposed design. This is to say, the surface to volume ratio and the volume of the new class of structures and their gyroid equivalent are equal. Models are built using CAD software and printed with UP mini 2.0 using acrylonitrile butadiene styrene (ABS) copolymer. Moreover, compression tests are conducted, using “MTS Criterion—Model 45”. The results show that after the phases of elasticity, relaxation and plasticity, the structure (three samples) is stable in the sense that it did not buckle nor collapse. Furthermore, reaching 7.35 mm of platen displacement (14.7% of strain) and 7.5 kN of resistance (3 MPa of equivalent stress), an additional progressive hardening is observed due to material densification and friction phenomena. A normalized comparison between the proposed structure and several lattice structures is conducted, showing a higher competitive behavior of the new design. The results of this study could possibly be a major contribution in the fields of biomechanics, aeronautic, and mechanical parts design.