A Weighted Residual Quadratic Acceleration Time Integration Method in Nonlinear Structural Dynamics

A new method is proposed for the direct time integration method for nonlinear structural dynamics problems. In the proposed method which includes an extensive family of direct time integration, the order of the time integration scheme is higher than the classical methods. This method assumes quadratic variation of the acceleration at each time step. The result obtained from this new higher order method is compared with two classical explicit methods; namely the central difference method and the Newmark's method (linear acceleration method). Due to increase in order of variations of acceleration, this method has higher accuracy than classical methods. Proposed method includes a family of conditionally stable methods. The numerical dispersion of the proposed method is far less than of those classical methods.