Analytical Modelling and Exact Solution for the Static Behaviour of Helical Beams: A Novel Approach

This study presents an exact analytical approach to model the static behaviour of helical beams made of elastic and isotropic materials, incorporating axial and shear deformation effects often neglected in existing literature. The behaviour of these beams is described by a set of twelve first-order differential equations, solved using the method of initial values. By considering cylindrical helical beams with constant cross-sections, this method formulates closed-form solutions, validated against prior studies and numerical results. Also, by performing parametric studies using this approach, the importance of geometric parameters, such as pitch angle and slenderness ratio, is demonstrated in influencing deformation behaviour. The results are found to be in very good agreement with the literature and finite element method, and they reveal that the proposed method is accurate and computationally efficient, making it a valuable tool for analysing and designing helical structures across engineering applications.