Analytical modeling and exact solution for the static behavior of helical beams: a novel approach

This study presents an exact analytical approach to model the static behavior of helical beams made of elastic and isotropic materials, incorporating axial and shear deformation effects that are often neglected in existing literature. The behavior of these beams is described by a set of 12 first-order differential equations, solved using the method of initial values. This formulation addresses a gap in the literature by providing an exact analytical solution for the static behavior of helical beams with axial and shear deformation effects. 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, as well as the effects of axial elongation and shear deformation on the static response, is demonstrated in influencing deformation behavior. 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 analyzing and designing helical structures across engineering applications.