From the trapezoidal rule to higher-order accurate and unconditionally stable time-integration method for structural dynamics

Abstract

Since the trapezoidal rule was originally proposed as the constant average acceleration method by Newmark, it has been modified to various forms. However, most of the modifications were limited to its numerical coefficients and, as a result, little change in the characteristics was obtained like numerical dissipation with the loss of accuracy. In this work, the constant average acceleration, which is a fundamental feature of the trapezoidal rule, is investigated and generalized. Using the generalization of average acceleration concept, a higher-order accurate and unconditionally stable time-integration method is developed. The stability analysis is carried out for a system of single degree of freedom. The analysis proves that the present method is unconditionally stable. To observe the accuracy of the method, several numerical tests are performed and the results are compared with the results from the trapezoidal rule and the exact solution. From the numerical tests, it has been known that the present method has a higher order accuracy.