An unconditionally stable explicit algorithm for structural dynamics

This paper proposes an unconditionally stable explicit algorithm for time integration of structural dynamics by utilizing the discrete control theory. New algorithm adopts the recursive formula of velocity and displacement of CR algorithm, and obtains the respective transfer function based on Z transformation. Further, the specific expressions of coefficients of recursive formula are derived according to the pole condition. Then, a variable s in the coefficients to control the period elongation is introduced, which is applied to adjust the accuracy of new algorithm. Theoretical analysis indicate that the new proposed unconditionally stable explicit algorithm possesses the properties of second accuracy, zero amplitude decay, non-overshoot and self-starting, and its period elongation can be controlled by the variable s. Moreover, the CR algorithm is a special case of the proposed algorithm. Finally, the stability limit of nonlinear stiffening system is determined, and variable interval corresponding to the higher accuracy of new algorithm is presented. Numerical examples demonstrate that in this interval of variable s, the accuracy of new algorithm is superior to that of Newmark constant average acceleration and CR algorithm. ©, 2015, Chinese Journal of Theoretical and Applied Mechanics Press. All right reserved.