Application of modified energy method in the nonlinear cyclic behavior of structures

Structural elements exhibit cyclic behavior or hysteresis under seismic loads; therefore, the analysis of this type of response is of great importance in Earthquake Engineering. On the other hand, due to the complexity of this nonlinear behavior and the absence of an explicit function to express the restoring-force regarding deformation, the modeling and analyzing of the phenomenon of hysteresis is one of the most complex problems in nonlinear dynamics of structures. In this research, the modified energy method is used as a numerical method to analyze this type of systems. To achieve the objectives of this research, a brief review on elastoplastic hysteresis models is initially considered. Then, by formulating the energy equilibrium equations for single-degree freedom structures with nonlinear material-cyclic behavior, the computer-implemented algorithm of this method is presented in a step-by-step manner. A simple single-degree-of-freedom example with bilinear-elastic stiffness under free vibration using the proposed method is provided for the reader's familiarity with the concept of the proposed method. Subsequently, a one-story structure and a multiple-degrees-of-freedom system with elastoplastic behavior are analyzed using the given method, and conventional numerical methods are utilized to verify the results. In general, the results of this study showed that this method has a good accuracy compared to other techniques in the analysis of hysteresis behavior of structures. In addition, this approach decreases the order in the governing equation of the problem; and, there is no need to define the additional adjustable parameters in numerical solution. On the whole, the presented technique with simplicity in computer execution can be used by creating a physical sense in the analyst to calculate the response of hysteresis structural systems.