An explicit time-domain method for non-stationary random analysis of nonlinear frame structures with plastic hinges

In this study, a novel approach for random vibration analysis of nonlinear frame structures under seismic random excitations is developed. The explicit time-domain method is improved in this approach by integrating the plastic hinge model, which can simulate the nonlinear behaviors caused by material property changes. Specifically, the hysteretic system’s equation of motion is constructed using auxiliary differential equations that govern the plastic rotational displacements and their corresponding hysteretic displacements. Additionally, by introducing the concept of equivalent excitations, an explicit iteration scheme for solving the equation of the hysteretic system is developed, in which the auxiliary differential equations are solved under the assumption that the plastic rotational velocity changes linearly with time between two adjacent time instants. Finally, by combining the Monte Carlo simulation method and the proposed explicit time-domain method, the non-stationary random responses of nonlinear frame structures can be obtained. As illustrated by numerical examples, the proposed method achieves satisfactory solution accuracy and efficiency when applied to nonlinear frame structures with plastic hinges. Moreover, the proposed iterative method resolves equations involving displacements describing the frame’s global state, plastic rotational displacements, and corresponding hysteretic parameters, introducing a novel concept for solving problems with nonlinear coupled variables of multiple types.