Design Framework for Optimization of Curvilinearly Stiffened Variable Stiffness Composite Laminates with Direct Fiber Angle Parameterization

Stiffened Variable Angle Tow (VAT) Laminates with optimized curvilinear fiber paths and curvilinear stiffeners are known to significantly improve structural performance over traditional laminates by increasing the buckling loads as a result of tailored stiffness and redistribution of the in-plane loads. Optimization of such laminates is highly non-convex and non-linear with a large design space. Optimization space can be made convex with the use of lamination parameters; however, that necessitates a second-level optimization for fiber path recovery. Further, the presence of manufacturing defects can highly impact the final performance of the design. Therefore, the current study focuses on designing a robust framework for the optimization of curvilinearly stiffened VAT composite laminates with fiber angles of each layer directly as design variables along with curvilinear stiffener layout and sizing parameters as well as manufacturability constraints. A novel approach is proposed to consider the fiber angles at the nodes of a coarse design mesh as design variables for steering the tow path and interpolate them to a finer analysis mesh using Lagrange shape functions. UGENS subroutine in Abaqus is employed to obtain the sectional forces and moments at each integration point for static and buckling analysis of the laminate. Tie constraints are used to enforce the displacement and rotation compatibility at the stiffener plate interface. Tow path recovery is done to obtain the realizable layout from the design fiber angles using a median based seeding strategy and parallel shifting techniques. The relationship between divergence of the 2D vector field obtained from the tow streamlines and the gap/overlap propagation is used to implement manufacturability constraints in the top-level optimization. Simulia's Isight package is used for integrating different analysis and data I/O components into a single optimization framework. Built-in particle swarm optimization (PSO) in Isight is used as the optimization algorithm. Several key design studies including maximum buckling load optimization of curvilinearly stiffened variable angle tow plates, with a central elliptical cutout, and subjected to constraints on the weight of the stiffener demonstrating the overall capabilities of the framework for efficient design of stiffened tow steered composite structures are presented along with other verification examples.