NONLINEAR DYNAMIC ANALYSIS OF BEAMS THROUGH FEM CORRATIONAL FORMULATION

Abstract

Knowledge of static and dynamic behavior is essential for the design of lighter and more slender structures without affecting, however, their safety and quality. Therefore, it becomes necessary to use more complex theories, as nonlinear formulations, avoiding simplifications in the analysis/design process. In this context, a co-rotational formulation of the Finite Element Method for the dynamic nonlinear analysis of beams, based on the Euler-Bernoulli theory, is presented. An incremental-iterative procedure with the Newmark's direct integration method and the standard Newton-Raphson method is employed to obtain the approximate solution of the nonlinear equations of motion. Numerical examples of beam problems with geometric nonlinearity found in the literature are presented to demonstrate the accuracy and efficiency of the algorithm implemented with the open-source software Scilab. The linear elastic constitutive relation for the material that constitutes the beams is adopted. As a dynamic response of the structures, the displacement versus time curves are shown.