A Co-rotation Based Secant Matrix Procedure for Elastic Postbuckling Analysis of Truss Structures

To investigate the geometrically nonlinear behavior of space structures using finite elements, the total Lagrangian (TL), updated Lagrangian (UL) and co-rotational (CR) procedures have been used by researchers. For 3D truss structures, the CR formulation has been reported to be computationally more efficient as it possesses the rigid body displacement components during deformations. In this paper, the secant stiffness matrix of truss element will be derived using a simple co-rotational, total Lagrangian (CR–TL) formulation. The incremental rotation matrix, which is the pivotal quantity in the CR formulation, is derived from geometric principles. The secant stiffness matrix is presented in terms of the natural degrees-of-freedom of the truss element. The efficiency and reliability of the present formulation is demonstrated in the solution of several truss problems involving the postbuckling behavior.