Numerical error assessment in nonlinear dynamic analysis of structures

Abstract

ABSTRACTThe complex nature of exciting forces in earthquake engineering applications mandates employing numerical methods to obtain structural response. Several numerical methods are used in earthquake engineering to solve the ordinary differential equation of motion. Previous studies assumed the appropriate time step as a constant fraction of natural period of the system disregarding period range. This study is concerned with assessing, by numerical experiment; the numerical error of commonly used schemes in nonlinear dynamic analyses and assessing their appropriateness for different excitations with different structural periods. The current investigation involved testing Newmark, HHT and HHT1 methods. The three methods were tested for nonlinear single degree of freedom system representing a typical concrete bridge structure. Three different exciting forces were used to test the schemes; half-sine pulse, harmonic force, and actual ground motion record. Three natural periods were used to conduct the experiment, representing short, medium and long period systems including the resonant condition. Three structural damping ratios, representing lightly, moderately and heavily damped systems, were used to assess the damping effect on the accuracy of the schemes. The results of this investigation indicated that commonly used assumption of time step as a constant fraction of natural period of the system disregarding the period range could result in significant numerical errors. The study also showed the significant effect of damping ratio of the system on the accuracy of the numerical schemes. The study presents a recommendation matrix of the most appropriate time step for each scheme for different applications and structural conditions.