#
Optimized One-Click Development for Topology-Optimized Structures^{ †}

^{*}

^{†}

## Abstract

**:**

## 1. Introduction

^{®}(developed by the Chair of Engineering Design and CAD, University of Bayreuth, Bayreuth, Germany) and is available at [43].

## 2. Materials and Methods

#### 2.1. Topology Optimization for Stiffness and Strength

^{®}was used, which was based on density methods for TO. While in general, the SIMP and rational approximation of material properties (RAMP) were implemented, SIMP was used for all optimizations presented in this article. The SIMP method thereby is given as

#### 2.2. Finite Spheres as Manufacturing Constraints

^{®}and was applied in the following experiments. Further information on the implementation and theory of the finite sphere concept can be found in [32] and the Z88Arion

^{®}documentation on [33].

#### 2.3. Two-Step Smoothing

#### 2.4. Example of Application

#### 2.5. Testing and Validation

## 3. Results

#### 3.1. Manufacturability of Design Proposals

#### 3.2. Experimental Testing

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 1.**The visualization of the presented one-click optimization approach. The one-click tool aims to re-place and to widely automate the steps of topology optimization, smoothing, data exchange and redesign and finite element analysis, which are shown inside the green shaded area.

**Figure 2.**Conceptual procedure of the topology optimization for stiffness and strength (TOSS) algorithm.

**Figure 3.**Determination of the effective radii with the tolerance angle; S denotes the center of gravity: (

**a**) the spheres with unadjusted radii collide in angle $t$; (

**b**) the radii are multiplied with $\mathrm{sin}t$; so that (

**c**) the spheres can pass without overlapping.

**Figure 4.**Spheres with (red) and without (green) manufacturing conflict potential to the grey sphere in manufacturing direction $s$ and manufacturing angle $\omega $.

**Figure 5.**Visualization of the conflict cones in the positive (+s) and negative (−s) direction. Conflict spheres in red and conflict-free spheres in green. The conflict spheres in the positive direction are stored in K

^{+}, while the conflict spheres in negative direction are stored in K

^{−}.

**Figure 8.**Double wishbone suspension with pushrod (red), rocker (green) and spring-damper unit (grey).

**Figure 11.**Tested configurations of the rocker: (

**a**) TO setup, the green areas are non-design spaces; and (

**b**) TO result without the consideration of the manufacturing conflicts.

**Figure 12.**Tested configurations of the rocker. (

**a**) reference; (

**b**) redesigned; (

**c**) smoothed; (

**d**) MaSmo.

**Figure 13.**TO results for various manufacturing rates $g$. All elements whose design variable is greater than 0.1 are displayed. Additionally, the number of iterations until convergence is noted (

**a**) $g=0.5$ iterations: 87; (

**b**) $g=0.6$, iterations: 41; (

**c**) $g=0.7$ iterations = 41; (

**d**) $g=0.8$ iterations: 99; (

**e**) $g=0.9$ iterations: 99; and (

**f**) $g=1.0$ iterations: 100.

**Figure 14.**TO results for various manufacturing angles $\omega $ at the manufacturing rate $g=0.7$, all elements whose design variable is greater than 0.1 are displayed. Additionally, the number of iterations until convergence is noted. (

**a**) $\omega =15\mathrm{deg}$, iterations: 76; (

**b**) $\omega =45\mathrm{deg}$, iterations: 41 (

**c**) $\omega =75\mathrm{deg}$, iterations: 100.

**Figure 15.**Printed and tested specimens: (

**a**) reference; (

**b**) redesigned; (

**c**) smoothed; and (

**d**) MaSmo.

**Figure 16.**Force–displacement plots for all configurations. The grey shaded lines are the experimental data, the green lines are predicted with the trained Gaussian process regression (gpr) model.

**Figure 17.**Comparison of the approximated force–displacement behavior of all configurations. The red dotted line indicates the level 75% of the reference’s maximum force.

**Figure 18.**Comparison of the maximum forces. The mean values are plotted together with the standard deviation. The difference from the reference is written in brackets in percent.

**Figure 19.**Comparison of the displacement at failure. The mean values are plotted together with the standard deviation. The difference from the reference is written in brackets in percent.

**Figure 20.**Comparison of the displacement at maximum force. The mean values are plotted together with the standard deviation. The difference from the reference is written in brackets in percent.

**Figure 21.**Comparison of the stiffness at maximum force. The mean values are plotted together with the standard deviation. The difference from the reference is written in brackets in percent.

**Table 1.**Force components for the chosen topology optimization (TO) problem. The values are based on the measurements of a formula student racecar [47].

Force Component | Value in N |
---|---|

$\overrightarrow{{F}_{D,x}}$ | 455 |

$\overrightarrow{{F}_{D,y}}$ | −750 |

$\overrightarrow{{F}_{p,x}}$ | 2960 |

$\overrightarrow{{F}_{p,y}}$ | 2770 |

**Table 2.**Overview of the TO settings of all configurations. Since reference is the initial design space, no TO is performed for this configuration. All volumes are referenced on the volume of the reference configuration.

Configuration | Algorithm | Manufacturing Constraints | Target Volume | Real Volume | Iterations |
---|---|---|---|---|---|

Reference | -- | -- | 100% | 100% | -- |

Redesigned | TOSS | no | 75% | 77.2% | 100 |

Smoothed | TOSS | no | 75% | 74.6% | 100 |

MaSmo | TOSS | Yes | 75% | 75.6% | 41 |

Feature | Value |
---|---|

Manufacturing direction | z axis |

Manufacturing rate | 0.7 |

Manufacturing angle | 45 deg. |

**Table 4.**Manufacturing data overview. The plastic volume is the actual volume used in production and is referenced on the reference plastic volume. The support volume of redesigned is used as a reference for the comparison of the needed support volume. The support volume ratio is defined by the ratio of the used support structures to the plastic volume.

Configuration | Print Time | Plastic Volume | Support Volume | Support Volume Ratio |
---|---|---|---|---|

Reference | 100% | 100% | -- | -- |

Redesigned | 103.2% | 92.0% | 100% | 0.76% |

Smoothed | 104.3% | 90.0% | 131.6% | 1.03% |

MaSmo | 95.3% | 88.9% | 52.6% | 0.42% |

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## Share and Cite

**MDPI and ACS Style**

Rosnitschek, T.; Hentschel, R.; Siegel, T.; Kleinschrodt, C.; Zimmermann, M.; Alber-Laukant, B.; Rieg, F.
Optimized One-Click Development for Topology-Optimized Structures. *Appl. Sci.* **2021**, *11*, 2400.
https://doi.org/10.3390/app11052400

**AMA Style**

Rosnitschek T, Hentschel R, Siegel T, Kleinschrodt C, Zimmermann M, Alber-Laukant B, Rieg F.
Optimized One-Click Development for Topology-Optimized Structures. *Applied Sciences*. 2021; 11(5):2400.
https://doi.org/10.3390/app11052400

**Chicago/Turabian Style**

Rosnitschek, Tobias, Rick Hentschel, Tobias Siegel, Claudia Kleinschrodt, Markus Zimmermann, Bettina Alber-Laukant, and Frank Rieg.
2021. "Optimized One-Click Development for Topology-Optimized Structures" *Applied Sciences* 11, no. 5: 2400.
https://doi.org/10.3390/app11052400