Antenna Bracket Design

TEKREVOLUTION is a high-tech service and consulting company from Italy that has extensive experience in R&D activities. One of their main activities is to explore intelligent additive manufacturing to provide higher stress-to-weight ratio solutions for the market.

Challenge

This use case is part of a bigger project done together with TekRevoultion and ESA to demonstrate the capabilities of Uptim.ai software to help during the optimization in topology optimization processes. The primary goal was to increase the robustness of the optimization, particularly for multiobjective purposes, in order to get a geometry performing well under different loads. The secondary objective was to reduce the manual hours of engineering experts when optimizing, reducing the complexity and the number of operations with a special focus on the postprocessing part. In this case, we will study an antenna bracket that substituted an original optimization use case (Vega C IS 2-3 FWD support). The allowable volume and the requirements for optimization were given by ESA.

Figure 1 – Computational mesh of the allowable volume of the antenna bracket (coarse mesh)

In particular, the mechanical requirements are the following:

• 1st main mode > 140 Hz
• Quasi-static loads: 40g in all directions
• 4 Ifs with the unit, modeled as a 0.4 kg concentrated mass at the center point of the holes

Solution

The Statistical Optimization feature works by generating iteratively surrogate models while reducing the domain of study to where the zone of interest (zone of optimum) is located. That way, the model keeps getting refined only where the maximum probability of having a good solution is located. This approach has two main benefits in comparison to standard optimization techniques. The first benefit is that the number of samples needed until convergence is much lower, resulting in a decreased computational cost. The second benefit is that as the result is not a single point, but a range of possible values, the solution provided is much more robust to final adjustments and changes.

In this case, a first FE model is realized using the Inspire interface (Figure 3.1). The input parameters used for this problem are:

• MEMBSIZ: The smallest size of an element of the structure
• STRESS: Maximum stress supported by each element of the structure
• theta & fi: Normalised normal vector of deposition plane in spherical coordinates

And the inquired outputs are:

• WCOMP: Weighted compliance index (minimized during topology optimization)
• MASS: Target mass
• FREQ: 1st mode frequency

Uptim.ai Statistical optimization was used to minimize the mass while being compliant with the constraint of the first natural frequency. Three iterations (i.e. models) were realized by Uptim SO. The simulations were done by coupling our software with OptiStruct, so we were automatically changing the input files, running the Optistruct, and reading its results to adaptively choose where the next sample would be in order to generate the model as efficiently as possible. In the following pictures, it can be seen the domain reduction for some of the inputs (the angles of the vector of deposition) into the zone where the optimum is located, iteration by iteration, as well as the behaviour of the mass (final main output).

Figure 2 – FI input range convergence

Figure 3 – THETA input range convergence

Figure 4 – MASS results convergence

As we can see in the previous pictures, we end up with a narrow range of possible solutions of the angles of deposition that end up with a considerable decrease in the final mass of the component. No matter which is the exact value inside that range, the mass that we will have will be in the green distribution of the last figure, and being well optimized. In general, we can see as well how the mass changes depending on the two angles of deposition, with the clean minimum zone identified.

Figure 5 – theta and fi detailed model

The optimum zone was consistent with the frequency requirement, as all the combinations of inputs led to a first natural mode higher than 140 Hz (viable solutions). So there was no real constraint on whether the angles of deposition were actually valid or not from the frequency side (Figure below).

Figure 6 – Frequency convergence (theta and fi)

Nevertheless, Optistruct was not able to converge from the stress side in the whole domain, finding a zone (where the Stress was lower to 21) where convergence was not guaranteed. There were still some points converging, but if chosen the optimum point with the stress inside the 20 - 21 range, a deeper analysis should be made to ensure convergence.

Figure 7 – Global convergence (stress)

The input distributions for the final iteration (Figure 3.3 to 3.6) led to a mass minimization range. The final optimized configuration was found to be 2.2 kg. The result in terms of the final net shape with the coarse initial mesh is shown in the following figure.

Figure 8 – Final net shape of antenna bracket (coarse mesh)

The mesh was then refined and a more detailed net shape was obtained and smoothed with Inspire, with the parameters suggested by our software. In the final printable geometry, a last simulation is made in order to verify that all the requirements are met.

Figure 9 – Final net shape of antenna bracket (refined mesh)

Benefits

• Reduction of the mass up to 9.6% (in comparison to using direct topology optimization from Optistruct)
• Increase in performance (frequency, stress and displacement)
• Ensuring robustness in the design
• Reducing the cost of postprocessing