Improved Method for the Dynamic Response of Bilinear Systems

A procedure is presented to eliminate the error introduced in the step-by-step numerical integration of the equations of motion of hysteretic bilinear systems subjected to earthquake excitations by abrupt changes in their load-deformation characteristics during a time step. The procedure can be incorporated into any of the commonly used numerical integration methods, and basically consists of the detection of changes in load-deformation behavior and the determination of the precise times at which such changes occur. Equations for the calculation of the aforementioned times are derived for the particular case of Newmark's constant acceleration method. A numerical analysis is carried out to evaluate the performance of the proposed procedure when compared with the corrective force approach employed in the computer program DRAIN-2D.