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A new time integration scheme is presented for solving the differential equation of motion with nonlinear stiffness. In this new implicit method, it is assumed that the acceleration varies quadratically within each time step. By increasing the order of acceleration, more terms of the Taylor series are used, which are expected to have responses with better accuracy than the classical methods. By considering this assumption and employing two parameters b and a, a new family of unconditionally stable schemes is obtained. The order of accuracy, numerical dissipation, and numerical dispersion are used to measure the accuracy of the proposed method. Second order accuracy is achieved for all values of b and a. The proposed method presents less dissipation at the lower modes in comparison with Newmark's average acceleration, Wilson-9, and generalized-a methods. Moreover, this second order accurate method can control numerical damping in the higher modes. The numerical dispersion of the proposed method is compared with three unconditionally stable methods, namely, Newmark's average acceleration, Wilson-9, and generalized-a methods. Furthermore, the overshooting effect of the proposed method is compared with these methods. By evaluating the computational time for analysis with similar time step duration, the proposed method is shown to be faster in comparison with the other methods.

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An explicit time integration method is presented for the linear and nonlinear dynamic analyses of structures. Using two parameters and employing the Taylor series expansion, a family of second-order accurate methods for the solution of dynamic problems is derived. The proposed scheme includes the central di®erence method as a special case, while damping is shown to exert no e®ect on the solution accuracy. The proposed method is featured by the following facts: (i) the relative period error is almost zero for speci¯c values of the parameters; (ii) the numerical dissipation contained can help¯lter out spurious high-frequency components; and (iii) the crucial lower modes are generally una®ected in the integration. Although the proposed method is conditionally stable, it has an appropriate region of stability, and is self-starting. The numerical tests indicate the improved performance of the proposed technique over the central di®erence method.

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