Finite Element Based Buckling Cross-Sectional Optimization for Composite Arrows

Abstract

In archery, dynamic buckling during the launch phase compromises the target accuracy of arrows. For both dynamic and quasi-static arrow buckling, the critical load depends upon the area moment of inertia of the cross-section which should be increased at constant arrow weight, by redistributing the material as far away from the principal point of the cross-section as possible, and while keeping the material thick enough to prevent local buckling. In this paper we present an effort to optimize the cross-sectional shape of a composite arrow shaft, using a finite element based, quasi static buckling analysis keeping the length and area of the cross-section constant. The composite column considered is assumed pinned at both ends and is assumed made with fibers oriented along the length of the column. Four cross-sectional shapes, tubular circular, tubular equilateral triangular, star shaped and star with beads are analyzed in this study. The composite column is modeled in ABAQUS, and the buckling load is determined by using the “Linear Perturbation, Buckle” analysis. The transition from global to local buckling characterized by a decrease in bucking load and change in the buckled shape of the column is determined for each cross-sectional shape. The point of transition marks the maximum load that can be sustained for that cross-sectional shape. The maximum load for all the cross-sections is determined and compared. The tubular circular cross-section composite column is found to provide the highest buckling load followed by the star with bead cross-section, star shaped cross-section and tubular equilateral triangular cross-section composite column in the respective order. Thus, of the shapes considered, the tubular circular cross-section is the optimum shape for the cross-section of the arrow shaft.