New Practical Approach to Nonlinear Dynamic Analysis of Structures: Refinement of Newmark’s and Wilson’s Classical Methods

Abstract

This paper presents a new method for direct time integration of nonlinear structural dynamic problems. In the proposed method, the order of time integration scheme is higher than the conventional Newmark’s family of methods. This method assumes second-order variation of the acceleration at each time step. Two variable parameters are used to increase the stability and accuracy of the method. The result obtained from this new higher-order method is compared with two implicit methods, namely the Wilson-θ and the Newmark’s average acceleration methods. The proposed method is an alternative quick method that can be written using matrix laboratory (MATLAB) for checking results from a more refined analysis or for a quick calculation with adequate accuracy.