Collaborative optimization for variable stiffness composite laminates using a fiber angle description method based on Archimedean spiral function

Abstract

When optimizing the fiber orientation of multilayer composite laminates, with the increasing number of layers, the number of design variables increases sharply, resulting in a large amount of computational cost. To address this challenge, this paper proposes a novel discrete fiber angle optimization method based on the Archimedean spiral function and applies it to a collaborative design framework of topology and fiber orientation. The proposed method uses the normal distribution function as the angle selection function in every layer. To prevent convergence issues in optimizing the fiber angle, a new candidate angle weighting formula is proposed. Further, a discrete fiber angle parameterization method based on the Archimedean spiral function for the thickness direction of laminates is presented, which requires only one variable to represent the fiber angle of any two layers in the element. To circumvent the issue of local optima and expand the design space, a collaborative optimization strategy is employed to improve the discrete fiber angle optimization results. Finally, the numerical examples indicate that in comparison to conventional approaches, the correlation of the proposed method with initial values is significantly reduced (σ2=0.00188). Under identical initial conditions, this method can improve the structural stiffness by over 20% at maximum.