Application of Timoshenko Beam Theory in Finite Element Simulation of Fiber-Reinforced Composite Material

Abstract:

The limbs of compound bows are subjected to highly complex and intensive mechanical loads throughout the entire shooting cycle. Due to the operation of the cam system, forces acting on the limbs may exceed the applied draw force by several times, particularly near maximum draw. Extreme dynamic loads can be generated during dry firing, which may result in sudden and often fiber-directional failure of composite limbs. Local stress levels are further increased by stress concentration effects arising from geometric and material inhomogeneities. In this study, the forces acting on the cam system and the bow limbs were determined through preliminary analytical calculations. The Euler–Bernoulli beam theory was applied to estimate limb deflection analytically. The analysis was refined using the Timoshenko beam model to account for shear deformation and cross-sectional rotation. Cross-sectional second moments of area and relevant material properties were determined to ensure accurate results. The calculated deflections, although small in magnitude, were shown to have a significant influence on the stress state of the limbs. Based on the numerical results, it was concluded that compound bow limbs operate close to, or in some cases beyond, their material limit under severe loading conditions.

• Periodical: Materials Science Forum (Volume 1199)
• Pages: 137-145
• DOI: https://doi.org/10.4028/p-NUawv9
• Online since: August 2026
• Authors: László József Mónus*, Enikő Réka Fábián
• Keywords: Compound Bow Limb, Euler-Bernoulli Beam Theory, Finite Element Simulation, Timoshenko Beam Theory, Vibration Frequency

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