Optimizing fiber paths of tow-steered laminated composites for parametric stability using isogeometric analysis and genetic algorithm

Abstract

An isogeometric formulation is presented for fiber path optimization of tow-steered composite laminates (TSCL) with minimal parametric instabilities. Here, the fiber path functions of a TSCL is expressed smoothly by Cp−1 continuous non-uniform rational B-splines (NURBS) for engineering shapes, providing accurate field solutions. In this way, the motion equations of a TSCL plate is developed based on the third-order shear deformation theory (TSDT) and the Bolotin’s approximation is used to determine the parametric instability region. Primarily, the accuracy and efficiency of presented framework is measured for a TSCL example with respect to the existing solutions. Then, the optimal fiber paths of TSCL plates are searched using the genetic algorithm (GA) for various geometries, force component combinations, and dynamic-to-static force ratios. Results reveal that the optimal fiber paths are not necessarily symmetric even for regular domains, demonstrating the non-uniform coupling of bending and twisting stiffness in TSCL plates. The optimal design of TSCL fiber paths necessitates the consistency of local stiffness distribution and the resultant bending–twisting mode shape, specially when the dynamic force is high with respect to the static one. Geometry, force component combination, and dynamic-to-static force ratio impose case-specific fiber paths for optimal TSCL plates, requiring both minimal deformation and instability opening.