Design and construction of modern FRP Japanese bows by an inverse modelling approach of the elastica theory

Abstract

Modern archery bows employ composite limbs of organic materials and fibre-reinforced plastics (FRP) to increase strength and durability in a lightweight structure. However, empirical methods are often employed for the manufacturing of the bows. We propose a systematic method for the design and fabrication of FRP bows based on an inverse modelling approach of the elastica theory, which significantly simplifies the analysis of the bow’s limb deformation. The construction materials are analysed by the three-point bending test and by strain gauges. We manufacture three asymmetric FRP Japanese bows with a length of 1.6 m, a force of 5 kgf, and different unbraced curvatures by using wood and glass fibre laminates. The excellent matching between the manufactured bows and the design is confirmed by a small discrepancy in the measurements of bending stress (RMSE < 8 MPa), final force (< 5%), and deformation (RMSE < 2 mm) of the bows. The inverse model demonstrates the use of FRP in bows traditionally manufactured with organic materials, by posing constraints to preserve their long-established shape. Compared to the try-and-cut approach, our method provides the sufficient requirements and failure criteria for the construction of a bow’s limb, without involving complex numerical simulations.