Research On Novel Robust Optimization Design Methods For Structures And Their Applications

The core of robust optimal design(ROD) for structures is to find the best design scheme to ensure that constraint conditions and output performance have enough robustness under external uncertainties, in which the weighted sum of the mean and standard deviation of the output performance is regarded as the objective function. The best optimization design results are then sought under the reliability constraints. For structures subjected to various uncertain factors, many researchers are employing ROD to reduce the effect of these uncertainties and improve the performance for structures. Thus, the ROD has been extensively applied to many fields, such as mechanical design, aerospace, civil engineering, processing and manufacturing, and vibration control. However, the available ROD methods depend on the selected weights from the engineers, and different weights can lead to very different design schemes; thus this shortcoming limits the engineering application of ROD. To circumvent these difficulties, a novel ROD model is proposed, and a novel algorithm with high accuracy and high solving speed is also presented, in which engineers are free of the choice for weights. Finally, the proposed approach is applied to the design for a printed circuit board. The details are summarized as follows:(1) Using standard deviation as the robustness metrics of output performance, a new ROD model is proposed, in which the product of performance’s mean and standard deviation is regarded as objective function, and reliability index greater than the designed reliability index is treated as constraint. Sparse grid method with high computational efficiency and precision is utilized to solve the proposed ROD model. A numerical example and an engineering example are employed to verify the feasibility and efficiency of the proposed model.(2) Using information entropy as the robustness metrics of output performance, a novel ROD model is proposed, in which the product of performance’s mean and entropy is regarded as objective function, and reliability index greater than the designed reliability index is treated as constraint. Kernel density estimation method are used to determine information entropy of output performance, and further the approximate function relationship between performance entropy and design variables are obtained by the linear fitting technology. Sparse grid method with high computational efficiency and precision is employed to evaluate the proposed ROD model. A numerical example and an engineering example are used to verify the feasibility and efficiency of the proposed model.(3)Finite element model of a printed circuit board is employed to demonstrate the practical application of the proposed ROD model, in which the product of mean and standard deviation for the maximum amplitude of printed circuit board at the first order nature frequency is treated as the objective function. The modal analysis and random vibration analysis of the printed circuit board model are done before and after the optimization. The finite element analysis results show the feasibility and validity of the proposed ROD model.