# Topology Optimization for Additive Manufacturing as an Enabler for Light Weight Flight Hardware

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## Abstract

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## 1. Introduction

## 2. Background

## 3. Holistic Process Flow

#### 3.1. Candidate Part Selection

#### 3.2. Topology Optimization for Additive Manufacturing

#### 3.3. FEM Design Verification

_{allw, AlSi10Mg}is the maximum allowable yield stress (design allowable), σ

_{vonMises}is the Von Mises stress obtained from FEM analysis, SF

_{yield}is the yield strength safety factor, and SF

_{AM}is the Additive Manufacturing conservatism safety factor. Equation (1) is used in subsequent sections to derive the Margin of Safety for each of the case studies presented.

#### 3.4. Additive Manufacturing

#### 3.5. Mechanical and Material Verification

## 4. Case Studies

## 5. Results

#### 5.1. Case Study 1: Star Tracker Camera Bracket

#### 5.1.1. Topology Optimization

#### 5.1.2. FEM Design Verification

_{peak.}Eigen frequencies in the range of 1–100 were calculated with the design restriction that the first eigenfrequency be greater than 140 Hz.

_{vonMises}equal to 110 MPa, $S{F}_{yield}$ equal to 1.1, $S{F}_{AM}$ = 1.5, and σ

_{allw},

_{AlSi10Mg}= 190 MPa, yields a MoS of 0.05. It should be reiterated, however, that this Margin of Safety includes a somewhat arbitrary Safety Factor for Additive Manufacturing equal to 1.5 that has been added in this study to alleviate fears for this new technology. It is felt that this additional safety factor will evolve to values that are closer to 1.0 in the future.

#### 5.1.3. Manufacturing

#### 5.1.4. Testing

#### 5.1.5. Case 1 Summary

#### 5.2. Case Study 2: SSTL Edge Insert

#### 5.2.1. Topology Optimization

#### 5.2.2. FEM Design Verification

_{vonMises}equal to 72.7 MPa, $S{F}_{yield}$ equal to 1.1, $S{F}_{AM}$ = 1.5, and σ

_{allw, AlSi10Mg}= 190 MPa, yields a MoS of 0.58. It is important to note that the calculated margin or safety also includes an AM safety factor of 1.5 to satisfy industrial concerns.

#### 5.2.3. Manufacturing and Testing

#### 5.2.4. Case 2 Summary

#### 5.3. Case Study 3: Lunar Lander Engine Mount

#### 5.3.1. Topology Optimization

#### 5.3.2. FEM Design Verification

_{RMS}method) in the xy plane and z planes of the spacecraft, respectively. Enveloping the two load cases, the maximum stress was found to be 111.2 MPa. Using values of $S{F}_{yield}$ equal to 1.1, $S{F}_{AM}$ = 1.5, and σ

_{allw, AlSi10Mg}= 190 MPa, a MoS of 0.04 is calculated. Hence, all stresses are well within the design allowables for the final optimized concept providing positive margin of safety, and hence according to the holistic process flow, this design is analytically verified and ready to be manufactured. The static equivalent load level for the z-excitation is 154 g out of plane and 25 g in plane and 36 g out of plane and 79 g in plane for the xy-excitation, respectively. Moreover, fatigue and shock analysis were also performed. Fatigue analysis has been done with the ESA software ESAFATIG v4.3.1a; the fatigue calculations are based on the linear damage accumulation (Palmgren-Miner) rule. The fatigue study required that four times the life needs to be shown, and the analysis resulted in 10.4 times life. The shock assessment was based on the ECSS “Point Source Excitation Method”. With a safety factor of 3 dB, a positive margin of 4.3 dB was determined from the analysis.

#### 5.3.3. Manufacturing

#### 5.3.4. Testing

#### 5.3.5. Case 3 Summary

## 6. Summary

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 12.**Overlay of nominal CAD geometry with fabricated part geometry obtained from CT scan data.

**Figure 13.**Schematic the edge insert cross section illustrating the macro-lattice supporting the top horizontal surface.

**Figure 19.**Results of the FEM analysis: Stress plot of the complete engine mount structure subjected to x/y excitation.

**Figure 20.**Results of the FEM analysis: Stress plot of the complete engine mount structure subjected to Z excitation.

Build Orientation | Ultimate Strength (MPa) | Yield Strength (MPa) | % Elongation | |
---|---|---|---|---|

Horizontal | Average | 392.98 | 244.93 | 6.60 |

Std. Dev. | 8.30 | 7.85 | 0.55 | |

Vertical | Average | 394.29 | 208.54 | 5.5 |

Std. Dev. | 1.63 | 2.24 | 0.58 |

Build Orientation | Ultimate Strength (MPa) | Yield Strength (MPa) | % Elongation | |
---|---|---|---|---|

Horizontal | Average | 396.2 | 259.6 | 8.1 |

Std. Dev. | 7.3 | 7.4 | 0.8 | |

Vertical | Average | 434.1 | 244.9 | 5.8 |

Std. Dev. | 11.8 | 9.0 | 0.7 |

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**MDPI and ACS Style**

Orme, M.; Madera, I.; Gschweitl, M.; Ferrari, M. Topology Optimization for Additive Manufacturing as an Enabler for Light Weight Flight Hardware. *Designs* **2018**, *2*, 51.
https://doi.org/10.3390/designs2040051

**AMA Style**

Orme M, Madera I, Gschweitl M, Ferrari M. Topology Optimization for Additive Manufacturing as an Enabler for Light Weight Flight Hardware. *Designs*. 2018; 2(4):51.
https://doi.org/10.3390/designs2040051

**Chicago/Turabian Style**

Orme, Melissa, Ivan Madera, Michael Gschweitl, and Michael Ferrari. 2018. "Topology Optimization for Additive Manufacturing as an Enabler for Light Weight Flight Hardware" *Designs* 2, no. 4: 51.
https://doi.org/10.3390/designs2040051