Structure-dependent improved Wilson-θ method with higher order of accuracy and controllable amplitude decay

Abstract

• Proposed method yields more accurate responses than Newmark's family of methods. • An important system property is inserted by using α to the acceleration formula. • The method reaches the unconditional stability if θ ≥ 1.38 is adopted. The Wilson-θ method has been proven to have unconditional stability as a numerical direct time integration method in structural dynamics when θ ≥ 1.37 is adopted. Notwithstanding this great advantage of the method, it has also been proven that the method suffers from two shortcomings: high amount of uncontrollable amplitude decay and period elongation. In other words, the unconditional stability allows time step to be stretched, but as the time step grows longer, amplitude decay and period elongation errors grow higher, resulting in a low level of accuracy. The improved version of the Wilson-θ method negates the disadvantages of the classic method by raising the order of acceleration to vary in quadratic scheme over time step domain and by introducing an accelerator coefficient to the acceleration formula in order to control the amount of amplitude decay and lessen the period elongation error. The stability and accuracy of the proposed method has been analyzed, and the results show that unconditional stability is obtained if θ ≥ 1.38 is adopted. A formula is derived for the accelerator coefficient to make it applicable to various types of structural dynamic problems. Numerical examples are presented to provide a practical assessment of the method, along with the classic Wilson-θ and other methods of similar class.