In order to make a large area survey, detect a large scale structure and understand dark energy, a large radio interference array with a large number of feeds is required. However, cost and deformation control are main considerations in designing a large antenna array. In this paper we designed a cylinder parabolic structure for antenna array 45m x 40m of "Tianlai" project in Xinjiang, China in 2015. In order to largely reduce weight and cost, the antenna was divided into many assemble units, their structure was optimized by MSC.Patran/Nastran and their reflector deformation under various load cases of gravity, snow and wind was analyzed. For the feed support, we compared different types of structure such as arch-bridge, tower, cable and pole, and by mechanical simulations we found that the arch-bridge structure is very helpful to achieve large span, decrease weight and improve stability, for example, the total weight of optimized structure can be reduced to 43.7% of before. Finally some deformation measurement and experiment methods were discussed, which can be extended to array 100m×100m in the future.