PSI - Issue 28

Florian Vlădulescu et al. / Procedia Structural Integrity 28 (2020) 637–647 Vl ă dulescu and Constantinescu / Structural Integrity Procedia 00 (2019) 000–000

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to the initial value of 839 Hz, this being in fact the main objective of the optimization analysis. The total deformation increased to 59.8 mm compared to 14.2 mm for the solid bracket.

Fig. 5. Material distribution after solving the lattice optimization analysis.

Fig. 6. Mode shape corresponding to the first natural frequency of the optimized lattice model.

3D printing allows the generation of parts with complex microstructures, sometimes different scales being present for a component. As mentioned in ANSYS Material Designer (2019c), the ratio between the involved length scales can be significant, and by using a single finite element model the problem of length scale differences (when reducing the cell size) will produce significant computation challenges. In such situations the standard approach is homogenization. Based on the assumption of a separation of scales, numerical homogenization is often used to model the lattice structures by means of equivalent material properties, as done by Jansen and Pierard (2020). In their work an industrial bracket is also used as a case study to analyse the efficiency of homogenization. ANSYS Material Designer (2019c) assumes that the material under consideration has a representative microscale structure, the representative volume element (RVE). This is a small volume of the material that is still large enough to exhibit the correct macroscopic material properties. For periodic materials, this can be easily identified as a unit cell. In a periodic material, this unit cell repeats itself in all three coordinate directions. Thus, it contains all the information about the material, and it is sufficient to consider only the behaviour of the single unit cell. If macroscopic properties remain fixed, the initial volume is likely suitable as an RVE. The homogenization process starts in ANSYS with modelling the RVE. This requires the creation of a simplified geometry, as well as the definition of material properties of the constituent materials. Subsequently, the geometry is meshed for finite element analysis. In this second design approach of the present study a homogenized model is obtained based on which a new modal analysis is performed. In this analysis, boundary conditions and finite element model characteristics (method, element type and size, etc.) are used identical to those in the initial modal analysis. Therefore, the second main stage of this study begins with the design of a material model whose properties for a cubic cell vary according to the lattice density. Such a material generates a file containing the nodal coordinates and the lattice variable density values corresponding to them, local values being shown in Fig. 7. The relative density is indicated in few points in the picture as to illustrate its distribution over the surface and section of the mounting bracket. The input data are used in a new modal analysis that will provide the natural frequencies, the first of them being the fundamental one, its increase being the main objective of the optimization process. After performing the modal analysis in which the homogenized model is generated starting from a cubic cell, it is established that the first natural frequency has a value of 1366 Hz, which increases considerably compared to the initial value of 839 Hz for the unoptimized model, this being in fact the main objective of optimization analysis. Now total displacement became 49.4 mm, being a little bit reduced from the value obtained with cubic cell. The weight of the bracket was reduced by more than half, from 45.5 kg to only 21.77 kg after optimization (lattice and homogenization gave practically the same mass value) with cubic cell. Probably the geometry of the