Layup Optimization of Composite Material Structures

Framework for the Buckling Optimization of Variable-Angle Tow Composite Plates

“…The entire distribution of spatial variable stiness of VAT laminates are not independent of each other and their feasible region, in terms of lamination parameters, forms a convex space [19]. Their values are required to be strictly constrained inside the feasible region to ensure a stable optimization procedure for the design of VAT laminates.…”

“…(19), the integrals are independent of material properties, plate dimensions and the design variables (Γ…”

“…An accurate boundary of the feasible region of lamination parameters is then important for the optimization of VAT laminates. Grenestedt [19] presented a set of equations that give an outer boundary for the feasible region of lamination parameters. In the current work, we derive a set of new explicit closed-form expressions that accurately denes the interdependent feasible region of ξ A 1,2 and ξ D 1,2 .…”

“…For buckling or vibration optimization problems, the objective function expressed in terms of lamination parameters is much less ill-conditioned (and can often be convex [19]) than using layer angles as the design variables. The revised objective function together with the convex design space reduces the complexity and computational time/eorts, eectively.…”

“…Later, Fukunaga and Sekine [18] further obtained closed-form expressions that can represent the feasible regions of the four in-plane and four out-of-plane lamination parameters. The pioneering work of Grenestedt and Gudmundson [19] proved the convexity of the feasible region of lamination parameters (also for the case of variable stiness) and proposed a variational approach to evaluate the feasible region numerically. In the design of VAT laminates, the value of each lamination parameter varies continuously across the planform and the corresponding feasibility constraints should be satised at every point.…”