# Optimization of Complex Structure Based on Human-Computer Interaction Method

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## Abstract

To solve the problem of structural optimization of complex structure under dynamic response constraints, a human-computer interaction method was proposed combined with advantages of human and computer in structural optimization, and being used in structural optimization of an aerospace assembly to verify its practicability and effectiveness. The method was mainly based on two steps: topology optimization by human-computer interaction and size optimization by computer. The aerospace assembly after structural optimization based on the method could satisfy the dynamic environment requirement and the results showed that first integral vibration frequency raised 41.1 % and magnification of acceleration dropped 25.2 % while the mass remained essentially unchanged. Also the experimental results compared with the simulation results showed that the relative error was less than 5 %, which proved the effectiveness of the simulation design. The human-computer interaction method might provide a reference for similar products not limited to aerospace field.

## Keywords

Structure optimization Human-computer interaction method Aerospace assembly Dynamic response constraints Topology optimization by human-computer interaction Size optimization by computer## 1 Introduction

Spacecraft will experience complex mechanics environment in the process of launching, and vibration is one of most important factors to be considered in the development phase of space products. Also spacecraft is strict to quality characteristics because the cost can decrease 10000 dollars as the weight reduces 1 kg [1], and one of the most important factors that limit human to explore space is the weight. For these many reasons, people often choose to use structural optimization technology to find the minimum mass and cost under the given constraints [2].

Although people wish the structure can be the most suitable in the initial process of the development, the space products either may not satisfy the constraints or have large useless material allowance constantly at the beginning. There are two methods to solve the problem; one is traditional means by manual work that the designer can modify the structure by experience again and again. The advantage of this way is that the direction is clear so the designer can adjust the project at any time to find the better structure. Also in the design process, the designer can consider the manufacturing and installing constraints adequately. However, the disadvantage also exists that this way may just find a good scheme but not the best structure. On the contrary, structural optimization by computer can find the best solutions through numerical iteration, but the disadvantage is that computing amount is too large for complex problem such as topology optimization for complex structure under dynamic response constraints.

Researching structural optimization problem under dynamic environment is of great importance [3], but the issue is difficult to solve because of complexity of the sensitivity analysis [4] and hugeness of the computing amount, and remain some theoretical problems to research [5], especially for the topology optimization [6, 7]. For this reason, people often translate the dynamic problems to the static problems according to the given principles. But the static method cannot reflect the influence of the free vibration item and damping, hence the situation often happens that static equivalent condition can satisfy the requirement but the dynamic condition cannot. Considering all above factors, a human-computer interaction method is proposed to solve the optimization of complex structure under dynamic response constraints.

## 2 The Human-Computer Interaction Method

There are frequency constraints, dynamic response constraints including dynamic response displacement constraints, dynamic response acceleration constraints, and dynamic response stress constraints and so on in dynamic environment structural optimization [8, 9]. And structural optimization has three levels, which are size optimization, shape optimization, and topology optimization. Topology optimization is often used in the concept phase in the optimization progress, and can make significant impact for the improvement of mechanical performance [10]. In consideration of the complexity of topology optimization by computer, we choose to take advantage of the manual work to modify the topology structure, in other words, this stage is topology optimization by human-computer interaction style. Then we can use size optimization to find the best size of the structure under the dynamic response constraints by guidelines method or mathematical programming approach methods.

Human-computer interaction method makes use of advantages of human and computer in structural optimization adequately [11, 12]. Its process concludes the following stages. Firstly, the finite element model can be created by finite element software and the model can be updated by some ways such as modal test to achieve a relatively accurate model. And modal analysis and vibration response analysis can be carried out based on the finite element model. From analysis of the above simulation results, we can get the weak parts of the structure and modify the topology structure to improve the mechanics characteristics. By some cycles of topology optimization by human-computer interaction, the structure will be better performed under the dynamic environment. Secondly, after the topology optimization by human-computer interaction, size optimization by computer is executed to find the best size for the structure to reach the best objective under the constraints. Thirdly, we will check the dynamic stress and other parameters to make sure that it can satisfy the requirement under the dynamic environment.

## 3 Structural Optimization of an Aerospace Assembly Using the Human-Computer Interaction Method

### 3.1 Problem Description

Sine test conditions of the aerospace assembly

Parameters (identification level) | Frequency(Hz) | |||
---|---|---|---|---|

4~10 | 10~17 | 17~75 | 75~100 | |

Amplitude 0~p | 13.09 mm | 3.22 g | 6.86 g | 4.13 g |

Loading direction | Three directions |

In this model, first integral vibration frequency (\( \text{f}_{\text{0}} \)) was set as 60 Hz, and magnification of dynamic response acceleration (a) was set as 5, yield limit of the material (\( \uptau_{\text{0}} \)) was 280 MPa.

### 3.2 Topology Optimization by Human-Computer Interaction

Parameters change chart of four topology structure

Parameters | Topo a | Topo b | Topo c | Topo d | Rate change a & d |
---|---|---|---|---|---|

First integral vibration frequency/Hz | 42.3 | 44.2 | 45.8 | 58.2 | +37.6 % |

Magnification of acceleration(node 516535) | 6.18 | 6.00 | 5.12 | 4.91 | −20.6 % |

Mass of the frame/kg | 17.49 | 17.25 | 17.57 | 17.93 | +4.7 % |

### 3.3 Size Optimization by Computer

Initial value and final value, maximum and minimum limit of size variable

Changes of cared parameters by simulations results after human-computer interaction optimization.

Parameters | Initial value | Optimization results | Rate change |
---|---|---|---|

First integral vibration frequency/Hz | 42.3 | 59.7 | +41.1 % |

Magnification of acceleration(node 516535) | 6.18 | 4.62 | −25.2 % |

Mass of the frame/kg | 17.49 | 19.44 | −0.3 % |

### 3.4 Check of Dynamic Response Stress

### 3.5 Experimental Verification

Comparison of the simulation results with the experimental results

Parameters | Simulation results | Experimental results | Relative error |
---|---|---|---|

First integral vibration frequency/Hz | 59.7 | 60.2 | 0.8 % |

Magnification of acceleration(node 516535) | 4.62 | 4.50 | 2.7 % |

Mass of the frame/kg | 19.44 | 19.35 | 0.5 % |

## 4 Conclusion

Combining with the advantages of human and computer in complex structural optimization, the proposed human-computer interaction method could make a good performance in complex assembly’s optimization. It also provided new ideas for structural optimization under dynamic response constraints to solve practical problems. In this paper the aerospace assembly could not satisfy the requirement under the dynamic response constraints primitively. But after the human-computer interaction structural optimization, the final structure could satisfy the dynamic environment requirement and results showed that first integral vibration frequency raised 41.1 % (from 42.3 Hz to 59.7 Hz) and magnification of acceleration dropped 25.2 % (from 6.12 to 4.62) while the mass remained essentially unchanged (from 17.49 kg to 17.44 kg). Also the experimental results compared with the simulation results showed that the relative error was less than 5 %, which proved the effectiveness of the simulation design. The human-computer interaction method might provide a reference for similar products that are not limited to aerospace field.

## Notes

### Acknowledgements

Funded by the manned space engineering of China is gratefully acknowledged. Besides, we are very grateful for prof. Qinghua Hu for providing the initial aerospace assembly model.

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