CAD-integrated stiffener sizing-topology design via force flow members (FFM)

Abstract

Stiffener design plays a crucial role in the lightweight design of stiffened panels. We propose a CAD-integrated stiffener design approach for shells. The problem is partitioned into two steps: (1) generating clear force flow members (FFM) based on the direction of principal stress, and (2) introducing a nodal variable-based sizing-topology optimization for further lightweight design enhancement. Specifically, we generate dense principal stress trajectory families using the iterative tracing technique, and extract FFM through hierarchical clustering. Generating high-precision principal stress trajectories on free-form surfaces is a challenging task. Our method differs from previous approaches in that we employ tensor transformations to convert principal stress directions from the 3D physical space into the 2D parameter space. We then create NURBS curve-based FFM in the 2D parameter space. The NURBS-based free-form deformations (NFFD) technique is utilized to map FFM from the 2D parameter space to the 3D physical space, ensuring FFMs are precise and watertight constructions of geometries. We propose a nodal variable-based sizing-topology method for the lightweight design of FFM. The heights of FFM control points are designated as design variables. Steadily eliminating pseudo-heights is achieved by using the Sigmoid function to penalize the design variables. Moreover, we introduce an NFFD-based isogeometric analysis method for stiffened panels modeled by NFFD-based FFM to realize the integration of design and analysis. The effectiveness and robustness of the presented method are demonstrated through various benchmarks and examples with industrial backgrounds. The proposed optimization framework exhibits strong application potential in the lightweight design of stiffened panels.