Based on structural features of cable-net of deployable antenna, a multiobjective shape optimization method is proposed to help to engineer antenna’s cable-net structure that has better deployment and adjustment properties. In this method, the multiobjective optimum mathematical model is built with lower nodes’ locations of cable-net as variables, the average stress ratio of cable elements and strain energy as objectives, and surface precision and natural frequency of cable-net as constraints. Sequential quadratic programming method is used to solve this nonlinear mathematical model in conditions with different weighting coefficients, and the results show the validity and effectiveness of the proposed method and model.

Cable-net structure has been widely used in space deployable antenna for light weight, high precision, and small stowed size [

Firstly, the optimum cable-net prestresses obtained on assumption that the antenna has been in its deployment state may not make sure it is easier for the antenna to be deployed. And if the antenna cannot be deployed smoothly, it will simply not work, so it is necessary to take a look at what kinds of cable-net prestresses that can ensure a high surface precision and make the antenna easier to be deployed. Secondly, there is much lower electrical energy for antenna cable-net system’s adjustment in space compared to that on earth, so the cable-net structure should be designed to make sure it can be easily adjusted in conditions with lower electrical energy. Thirdly, for antenna’s cable-net system, conventional optimization methods with feasible prestresses as objective cannot improve its deployment and adjustment properties, so the structural design method that can attain these goals should be studied carefully.

Based on the above considerations, a new design formulation with a multiobjective optimum mathematical model is proposed here to optimize cable-net’s shape to improve antenna’s deployment and adjustment properties. Because the optimum mathematical model is complex and nonlinear, sequential quadratic programming method is used to solve it. And in this multiobjective optimization, we can change weighting coefficients of objectives to meet different demands for practical necessity.

Structure of cable-net deployable antenna studied in this paper is shown in Figure

Structure of cable-net deployable antenna.

Structure of single cable-net.

As shown in Figure

If it is considered that all cable elements have the same cross-sectional area, the smaller the average stress ratio is the more easily the antenna will be deployed, so we set the minimum average stress ratio as one objective.

In space, lower electrical energy cannot provide large cable tensions for antenna deployment, and it cannot provide enough energy for antenna adjustment as well. So in order to make the cable-net system easier to be adjusted, it is needed to get larger structural deformations in conditions with small adjusting force to increase cable-net system’s adjustment property. We choose strain energy

The larger cable-net’s strain energy is the smaller its rigidity is, and this represents a better adjustment property for the cable-net system. So the maximum strain energy is set as another objective here.

High surface precision can make sure deployable antenna works well in space [

There may be vibrations when deployable antenna is deploying or deflecting in space. In order to protect antenna from damage by these vibrations, it is needed to make sure antenna’s natural frequency is higher than excited frequency. So we choose antenna’s natural frequency as another constraint here.

The above objectives are closely related to shape of cable-net system, so conventional optimization with only the cable elements’ cross-sectional area as variables is not suitable for the problem here. For this reason we choose cable nodes locations as the new variables. Because upper cable nodes are all on the surface of antenna’s reflector, and their locations cannot be freely changed, only locations of lower cable nodes are set as the variables.

As shown in Figure

We can change single cable-net shape by adjusting

Based on the above considerations, we establish the optimum mathematical model below:

Dimension and order are very different between the average stress ratio

We use weighting coefficients method [

The optimization for single cable-net shown in Figure ^{11} N/m^{2}, 1 mm, and 1.44 × 10^{3} kg/m^{3}. Electrical energy is lower in space; it cannot provide large pretension for cable-net, so each cable element pretension is just set at 50 N for calculations below. The constraints are

First, we solve the optimum mathematical model in conditions with

The optimum structure in condition with

We can also adjust weighting coefficients

The optimum structure in condition with

The optimum results in condition with

The iteration process of the average stress ratio

The iteration process of strain energy

In this paper, we establish the multiobjective optimum mathematical model of the single cable-net first. Then we normalize objectives and combine them to form a single objective by using weighting coefficients method. Later on we use sequential quadratic programming method to solve this single objective problem and obtain the optimum results in conditions with different weighting coefficients. These results suggest that the average stress ratio is sensitive to the nodes locations of lower cable elements on the left side of the structure.

Conventional optimization method with only cable elements’ prestresses as variables cannot improve deployable antenna’s deployment and adjustment properties to suit conditions like lower electrical energy in space, so optimizing cable-net’s shape to get higher deployment and adjustment properties will be a good way for deployable antenna. And the optimization processes of objectives show the validity and effectiveness of the proposed method and model.

The authors have no conflict of interests to declare.

Financial supports by Xi’an FANYI University (BK001), Shaanxi Province Department of Education (14JK2040), are gratefully acknowledged.