Design optimization of flexible kerf structures under quasi-static loading

Kerfing (relief cutting) is a technique that creates patterns of slender segments within planar surfaces. This study suggests using an optimization approach to determine the best kerf cell geometry within a surface of kerf cells (kerf panel). In finite element modeling, a beam element model is used, and the flexibility of these unit cells depends upon the material's elastic modulus and the cell's geometrical parameters. The distance between the cuts (tof f), the width of each cut beam (b), and the cut density (def f) were taken as the design variables of the optimization loop. In addition to the, cut shape (triangular, hexagonal, rectangular), the total number of unit kerf cells, cut thickness (a), and material properties are taken as inputs. The study uses a genetic algorithm, and the objective function is to minimize the coefficient of variation, which is a statistical measure that ensures that the stress distribution throughout the entire kerf structure is as uniform as possible. A nonlinear constraint enforces that the maximum von Mises stress acting on the kerf structure should not exceed a designer-specified limit. Case studies include optimizing kerf panels to uniformize stress distribution with different quasi-static loading conditions and minimum peak stresses induced. The results suggest that, although kerfing increases the flexibility in the structure, it reduces its load-carrying ability. However, the advantage of kerfing lies in its panels' ability to propagate stress through deformation, resulting in lower maximum stress and more uniformly distributed stress compared to panels designed by intuition or experience.