Theory of Three dimensional Helical Curved Beams with Variable Curvatures

Abstract

The analytical solution are derived for a general 3-D helical curved beam. The equilibrium equations are listed as twelve ordinary differential equations. All force, moment, rotation and displacement components form a set of differential equations of the same pattern. Once the curvature and torsion are specified, the analytical solutions can be derived, if the pattern of differential equations can be solved. Helical curved is found to be solvable. The analytical solutions of 2-D curves of circular, elliptical, cycloid, cantenry, parabolic curves are demonstrated here. The analytical solution of 3-D helical curve with variable curvature is also demonstrated.