In order to obtain structural dynamic response,a new step-by-step integration method was presented. Thismethod was introduced by quadratic Lagrangian interpolation of the nodal displacements within local time domain. Single parameters θ was varied to obtain good stability and accuracy. This method is characterized with good stability, quadric precision, self-starting and simple numerical format. Compared with the methods of Newmark,Wilson, and precise integration at different θ, this method is more accurate and reliable.
