Lattice structure optimization and homogenization through finite element analyses

Abstract

Lattice topology optimization can stimulate the design of new materials with spatially dependent properties with composite parts or three-dimensional printed components. The present work considers a mounting bracket for an industrial robotic arm as a case study, having as the main objective the increase of the fundamental frequency and secondly its mass reduction. Two design approaches were considered by using the ANSYS software: the first stage optimized the orthotropic lattice material by establishing an optimal variable cubic cell lattice density distribution in the geometric model; the second stage used a homogenized model based on the lattice optimization resulted from the previous stage and considered different volume fractions and variable density for four different types of cells. Homogenization increased the stiffness of the bracket by using the same cubic lattice cell and the fundamental frequency increased from 1227 Hz obtained with lattice optimization to 1366 Hz after homogenization. For the unoptimized bracket the fundamental frequency was only 839 Hz. The mass was reduced to more than half. The most effective proved to be the midpoint lattice cell as by homogenization the mass was reduced from 45.5 kg to 18.22 kg.

Homogenization Methods of Lattice Materials

“…Aside from improving efficiency, recent and future homogenization efforts are focused on structural optimization. Homogenization, in combination with optimization methods, has been shown to improve the efficiency of the optimization procedure as well as the overall performance of a lattice structure [43][44][45][46]. The homogenization method for a structural optimization procedure has been shown to dramatically increase stiffness [44], structural compliance [45], structural vibration [43], and energy absorption [46].…”

Simulating Bioresorbable Lattice Structures to Enable Time-Dependent Stiffness in Fracture Fixation Devices

“…To reduce this computational time, simplifications to lattice structures are often made. Alternatively, homogenisation can be used to upscale the application of lattices structures in FEA (Tollenaere and Caillerie, 1998;Alwattar and Mian, 2019;Vlădulescu and Constantinescu, 2020). Homogenisation aims to determine the macroscopic mechanical properties of the lattice from the mesoscale properties of its unit cell (Arabnejad and Pasini, 2013;Omairey, Dunning and Sriramula, 2019).…”

Characterization of mechanical equivalent properties for node enhanced graded lattice structure

“…The homogenization theory is a feasible way to study composite structures, which was widely used in the study of the equivalent mechanical properties of composite materials, the equivalent mechanical parameters of the lattice structure in the linear elastic phase can be obtained by establishing its microscopic representative volume element (RVE) and applying characteristic boundary conditions to the RVE [24]. At present, the commonly used homogenization theory methods to study the equivalent elastic mechanical properties mainly: empirical formula method [25,26], self-consistent method [27], RVE method [28][29][30], asymptotic homogenization method [18], etc. The RVE method is simple and easy to realize in the finite element analysis software, so it was widely used in the mechanical property analysis of periodic porous materials [2].…”