A Novel Approach for Buckling Analysis of Pretwisted Spatially Curved Beams by State Equations

Based on force equilibrium and rigid body considerations, a novel approach is proposed for deriving the state equations and then the buckling equations of pretwisted spatially curved beams. Based on statical consideration of an infinitesimal element from the last calculated configuration C-1 to the current configuration C-2, a set of condition equations for the state matrix is derived. Next, by enforcing the rigid body rule for the beam, another set of condition equations for the state matrix is derived. From these two sets of equations, the state matrix of the beam is derived that leads directly to the buckling differential equations. The merit of the proposed approach is that it only requires simple differential and matrix operations. No hidden errors are possible because no higher-order terms need to be treated. In addition, a direct link is established between the straight and curved beam theories. Finally, examples are provided to demonstrate the application of the theory to the buckling analysis of various curved beams, including the helical ones.