Multi-Objective Robust Optimization Method for CFRP Laminates Based on a Dual Dimensionality Reduction Strategy

This paper presents a robust multi-objective optimization method for a symmetric carbon fiber reinforced polymer laminate under uniaxial tension. The study focuses on the combined design problem of failure strength and failure displacement under material uncertainty. A fast structural response model is built by using classical laminate theory, and the Hashin failure criterion is used to predict the first-failure state of the laminate. The model takes uncertain material properties into account, so it can describe the effect of random changes in stiffness and strength on the structural response. To reduce the computational cost, the method uses a dual reduction strategy. The first step reduces the parameter space. Latin hypercube sampling is used to generate random samples, and Spearman correlation analysis is used to identify the key uncertain parameters. The second step reduces the sample space. K-means clustering is used to group the reduced samples and generate representative scenarios. Based on these scenarios, the study defines robust failure strength and robust failure displacement by combining the mean value and the standard deviation of the responses. A multi-objective genetic algorithm is then used to search for the Pareto solution set. After that, two single-objective optimizations are carried out to obtain the best strength and the best displacement, and these two values are used to form an ideal point. The two objectives are normalized, and the Pareto point with the smallest distance to the ideal point is selected as the final design. The results show that the proposed method can capture the positive relation between failure strength and failure displacement, identify the main uncertain parameters that control the response change, and provide a balanced design with good strength and displacement performance under uncertainty.