Numerical Optimization Journal

[Jenette Bregantini]

Aimsand Scope

This journal endeavors to publish research of broad interests in applied and numerical optimization. One volume is published each year, and each volume consists of three issues (April, August, December).

Infill parameters are significant with regard to the overall cost and saving material while printing a 3D model. When it comes to printing time, we can decrease the printing time by altering the infill, which also reduces the total process extent. Choosing the right filling parameters affects the strength of the printed model. In this research, the effect of filling density and infill pattern on the fatigue lifetime of cylindrical polylactic acid (PLA) samples was investigated with finite element modeling and analysis. This causes the lattice structure to be considered macro-scale porosity in the additive manufacturing process. Due to the need for multi-objective optimization of several functions at the same time and the inevitable sacrifice of other objectives, the decision was to obtain a set of compromise solutions according to the Pareto-optimal solution technique or the Pareto non-inferior solution approach. As a result, a horizontally printed rectangular pattern with 60% filling was preferred over the four patterns including honeycomb, triangular, regular octagon, and irregular octagon by considering the sum of mass changes and fatigue lifetime changes, and distance from the optimal point, which is the lightest structure with the maximum fatigue lifetime as an objective function with an emphasis on mass as an important parameter in designing scaffolds and biomedical structures. A new structure was also proposed by performing a structural optimization process using computer-aided design tools and also, computer-aided engineering software by Dassault systems. Finally, the selected samples were printed and their 3D printing quality was investigated using field emission scanning electron microscopy inspection.

Copyright: 2023 Dadashi, Azadi. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Funding: The authors would like to acknowledge the financial support of the Iran Small Industries and Industrial Parks Organization (ISIPO) for this project under grant number of 23607.

The functionality of a fabricated component relies on the combination of properties and geometry, achieved through a series of fabrication techniques [1]. Additive manufacturing (AM) processes offer advantages such as complex 3D geometries and flexible construction of layered structures [2]. Tailoring the build formulation allows for gradual changes in composition or lattice structures [3, 4]. For instance, Kumar et al. [5, 6] compared multi-blended and hybrid blended PLA matrix in 3D-printed tensile specimens, finding superior mechanical and morphological properties in the multi-blended matrix, reflecting the growing interest in exploring the potential of additive manufacturing.

In order to further increase the mechanical properties of parts fabricated by AM, designing and optimizing approaches have been introduced and developed at various scales. Specifically, on the macroscale, structural optimizations including shape, size, and topology optimization techniques could be considered for guiding the component design [23, 24]. Between these methods, polymeric composites can achieve their maximum potential by AM-driven TO [25]. Manufacturing constraints such as minimum size and connectivity limit the optimization according to the manufacturing ability [26]. The anisotropic material property, besides manufacturing constraints, is another parameter that should be applied during the process of designing and optimizing [27]. A transversely isotropic material model and solid anisotropic material with penalization coupled with an AM-driven topology optimization technique were proposed by Li et al. [28, 29]. Due to the layered fabrication process, they achieved mechanical improvement in stiffness and strength because of taking advantage of anisotropy. Wu et al. [30] presented a novel method for generating simultaneously optimized solid shell and porous infill in the context of maximum stiffness topology optimization. A material interpolation model, upon which the compliance is minimized, unified the resulting intermediate density distributions while all the fibers follow the direction of the principal stress.

Fountas et al. [41] examined the performance of different swarm-based evolutionary algorithms in optimizing single and multi-objective problems related to additive manufacturing, specifically fused deposition modeling (FDM). The results showed that algorithms do not perform equally when applied to different optimization problems, and the quality of Pareto non-dominated solutions is an important indicator for multi-objective problems. Yodo and Dey [42] introduced multi-objective optimization methods based on evolutionary algorithms to optimize FDM process parameters, leading to Pareto-optimal solutions for decision-makers.

The article discusses the multi-objective numerical optimization of 3D-printed polylactic acid (PLA) bio-metamaterial. The optimization takes into account the factors of topology, filling pattern, and infill density in order to improve the fatigue lifetime and mass of the material. Therefore, the novelties of the study are as follows,

Manufacturing parameters have a significant impact on material response, particularly for polymers [47, 48]. For example, it was reported that the Poisson ratio is influenced by infill density [49]. However, in this study, the material properties of filament were used and the investigation of other parameters was not included. Density, elastic module, yield strength, ultimate tensile strength, and Poisson ratio were obtained from technical datasheets provided by the material manufacturer. Based on Table 1, these properties are typically reported by the manufacturer based on standard testing methods [47]. Though, endurance limit, which refers to the maximum stress amplitude that a material can withstand for a given number of cycles without failure, cannot be obtained from technical datasheets and requires experimental testing. The endurance limit used in this study was obtained experimentally from the reference [48]. It should be noted that YouSu brand polylactic acid (PLA) filament, was used in component fabrication for 3D printing. The properties of 3D printed parts can differ from those of the raw filament material. For example, while the density of PLA filament was typically reported as 1.24 g/cm3 in manufacturer datasheets based on the ASTM D792 standard test method, 3D printed parts can have a different density due to their meta-structure. Additionally, the tensile module and yield strength of PLA filament are reported as 3.5 GPa and 60 MPa, respectively, based on ASTM D1238 standard test method. However, 3D printed parts may exhibit different values for these properties due to the complex interplay of factors such as infill percentage, layer height, printing speed, and other printing parameters. The endurance limit for 95% probability of survival and determined in terms of maximum stress and extrapolated at 2 million cycles to failure cycles, is considered equal to 0.1 final stress [48].

The compressive and tensile behaviors of PLA are usually considered to be the same, but some studies have focused specifically on the compressive behavior of PLA. These studies aim to better understand how PLA responds to compressive forces and how it can be used in applications where compression is a dominant mode of loading, such as in bone tissue engineering and orthopedics [50, 51].

Structural optimization is an iterative technique that could help the refinement of designs. Then, a result of the proper-designed structural optimization could be a lightweight part, which has durable properties. An integrated computer-aided design (CAD) and computer-aided engineering (CAE) workflow by Dassault systems was proposed (Fig 1).

The use of additive manufacturing enables the fabrication of different patterns with varying mechanical properties. The filling parameters have a direct effect on the response of the metamaterials to external loadings. For instance, a recent study [52] on metal functionally graded gyroids employed three design methods (thickness graded, size graded, and uniform) to provide a map of the mechanical properties of stainless-steel scaffolds. In the proposed study, we selected five infill patterns, including honeycomb, rectangular, triangular, irregular octagon [52], and regular octagon [52] to investigate their effect on fatigue properties and mass, and the results suggest that further investigations on other patterns may be necessary, to compare the fatigue behavior. The infill patterns used in this study are shown in Fig 2.

Based on the flow chart, a geometric model of the structure should be initially prepared in CAD software, including SolidWorks or Catia. Considering Fig 3, filling densities of 40%, 60%, 80%, and 100% were also designed in the section of a cylinder with an outer diameter of 9 mm and a height of 78 mm, by SolidWorks software. To achieve desired filling densities these geometries were arranged next to each other at different distances. In addition, two solid layers are considered as a perimeter with a width of 0.4 mm for each layer [53].

A finite element model is fabricated in SIMULIA- ABAQUS for stress analysis besides the topology optimization. To calculate bending stress according to the rotating-bending fatigue testing method [54], the samples were subjected to a 10 N load at the free end of a cantilever which is clamped at the other end; therefore, the displacements of the supported end are constrained in three directions (Fig 4(A)). In the rotating-bending test, a common method used to evaluate the high cycle fatigue behavior of materials, the specimen is subjected to cyclic loading through rotational motion. During the rotating-bending test, the applied stress levels are typically kept below the yield strength of the material. This ensures that the deformation experienced by the specimen remains within the elastic range (

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