Advanced lamination parameter interpolation and extrapolation methods for designing manufacturable variable stiffness laminates

The design of variable stiffness laminates requires efficient methodologies due to the increased number of optimization variables associated with curvilinear fiber paths. Here, this need is addressed by the development of two novel approaches: the lamination parameter extrapolation method (LPEM) and the relaxed lamination parameter interpolation method (RLPIM). These techniques build on the previously proposed lamination parameter interpolation method (LPIM), and collectively they form a spectrum of approaches that differ in optimization capacity, conservativeness regarding fiber curvature constraints, and computational cost. The resulting governing equations are solved using the spectral Chebyshev method to further improve the efficiency of the optimization process. The case studies demonstrate the effectiveness and unique properties of the developed algorithms.