An efficient time-integration method for nonlinear dynamic analysis of solids and structures

This paper presents an efficient time-integration method for obtaining reliable solutions to the second-order nonlinear dynamic problems in structural engineering. This method employs both the backward-acceleration differentiation formula and the trapezoidal rule, resulting in a self-starting, single step, second-order accurate algorithm. With the same computational effort as the trapezoidal rule, the proposed method remains stable in large deformation and long time range solutions even when the trapezoidal rule fails. Meanwhile, the proposed method has the following characteristics： （1） it is applicable to linear as well as general nonlinear analyses; （2） it does not involve additional variables （e.g. Lagrange multipliers） and artificial parameters; （3） it is a single-solver algorithm at the discrete time points with symmetric effective stiffness matrix and effective load vectors; and （4） it is easy to implement in an existing computational software. Some numerical results indicate that the proposed method is a powerful tool with some notable features for practical nonlinear dynamic analyses.