Multi-objective optimization of variable stiffness laminated plates modeled using Bézier curves

In this paper, intuitive fiber path definition methods using cubic and quadratic Bézier curves are proposed for variable stiffness (VS) laminates designed with Direct Fiber Path Parameterization (DFPP) technique. These methods construct fiber paths with nonlinear angle variation defined by simple design variables that are segment/station angles and multipliers/curvature. At its simplest, balanced symmetric VS laminates defined with two segment/station angles are illustrated, implemented in finite element model under uniaxial compression, and optimized using surrogate based multi-objective non-dominated sorting genetic algorithm (NSGA-II) for maximum buckling load and stiffness. The optimization results of VS laminates using cubic Bézier interpolation and quadratic Bézier approximation curves as fiber paths are compared for three different plate sizes and boundary conditions. The largest simply supported VS laminate that uses cubic Bézier curves of constant curvature as fiber path shows 103% increase in buckling load against 44% reduction in stiffness compared to quasi-isotropic laminate.