Accuracy Evaluation of Numerical Methods in Linear and Nonlinear Dynamic Response of MDOF Structures

In order to solve partial differential equation of motion for damped and undamped systems, series of techniques have been proposed. Generally a standard procedure is utilized to calculate exact solution of PDE. But when the order of matrices goes larger enough, the exact solution becomes more expensive. Hence numerical methods such as direct integration method and mode superposition will be considered. Some of these methods are conditionally stable and two errors; period shift and amplitude will occur. In this research the accuracy and reliability of prevalent numerical methods have been evaluated for MDOF structures. To evaluate the nodal response, a code has been developed by the authors and roles of time step size and critical time step have been analyzed. The results show that time step size often has a key role in increasing accuracy. Also by selection of minimum time step, AD error occurs but there is an optimum time step in which, minimum AD and AI errors occurred.

Accuracy Evaluation of Numerical Methods in Linear and Nonlinear Dynamic Response of MDOF Structures Keywords:

Direct Integration Method , Amplitude error. Period Shift , Time Step Size