Velocity based elements for the quasi-static analysis of beams and framesKusuma Chandrashekhara, Sudhanva (Avtor) Zupan, Dejan (Avtor) beam elementspath followingarc-length methodIn the present work, we propose the extension of the equilibrium equation based on the velocity based formulation with the introduction of an arc-length constraint. With the configuration variables defined in terms of time dependent quantities, the arc-length parameter in the original arc-length constraint equation can be replaced by increment of time step. Additionally, the constraint equation based on arc-length control is employed in its originally defined differential form. This eases the extension of the system of equations and the procedure can be applied in conjunction with the Newton-Raphson method. The proposed method also provides a flexibility to implement the stepsize control and in the present approach, we employ the local error control to determine the new step-size. The proposed method serves as a starting point in the post-critical analysis of the structures and aims at demonstrating the nonlinear responses in post-buckling regimes.20212021-10-21 14:54:00Zbornik132332UDK: 531:524.072(043)COBISS_ID: 80897795OceCobissID: 74786051sl