Extended implicit integration process by utilizing nonlinear dynamics in finite element

This paper proposes a new direct numerical integration algorithm for solving equation of motion in structural dynamics problems with nonlinear stiffness. The new implicit method\'s degree of accuracy is higher than that of existing methods due to the higher order of the acceleration. Two parameters are defined, leading to a new family of unconditionally stable methods, which helps to take greater time steps in integration and eliminate concerns about the duration of solving. The method developed can be utilized for a number of solid plane finite elements, examples of which are given to compare the proposed method with existing ones. The results indicate the superiority of the proposed method.