Study On Structural Robust Optimization Based On Reanalysis Technique

Various uncertain information always exists in structural analysis and design, which can not only bring fluctuations to the performance of the structure but also lead to failure to the structural function. Therefore, at the design stage, quantitative information on these uncertainties must be considered to reduce the sensitivity. Robust design is one of the important methods to analyze uncertain information, which has been valued and applied in the electronics, machinery, etc. In this paper, we mainly focus on structural robust optimization in the practical engineering applications and make it work for the antenna structure optimization. The details are as follows:1. As structural robust optimization needs a large amount of computation efforts, we propose to introduce reanalysis technique into the robustness analysis.2. Two reanalysis methods which are binomial series approximation and combination approximation were compared theoretically and numerically. Based on Gauss quadrature method, the former is introduced into robustness analysis, and then the quadrature formula based on the binomial series approximation is given. At last, the computational efficiency and accuracy of the proposed method are compared with other methods by using two examples.3. The sensitivity analysis of the structural robustness with respect to design variables is investigated in detail. The sensitivity calculation formulas of the mean and variance vectors of the structural displacements is derived based on Gauss-Hermite quadrature combined with binomial series approximation. When we use this method, reanalysis is no longer needed for sensitivity analysis. Then, to avoid storing large matrices, a simplified differentiation method is also proposed which can be used when the variances of the input random variables are relatively small.4. The tolerance optimization model of antenna structures is established by using the above mentioned methods. As an example, an 8-meter antenna backup structure is optimized to obtain optimal tolerance values of the cross-sectional areas of the backup bars. The results show that robust optimization design can effectively reduce the variance of the reflector surface precision thus increase its robustness.