Study On The Application Of Explicit Integration Formula In Finite Element Simulation Of Wave Motion

For numerical computation of earthquake responses of large-scale structure and complex site, especially non-linear response, the use of explicit algorithms is generally preferred over implicit algorithms in view of the amount of computational time. An explicit integration formula used to solve dynamic equation of damped structure, suggested by Li Xiaojun and others, has not only two-order calculating accuracy as that of the central differential integration formula, but also general applicability. In one hand, the integration formula can be applied to solve dynamic problem of system with any damping, on the other hand, when the integration formula is applied to the numerical analysis of wave motion in infinite space, the numerical dissipation of the formula can depress or eliminate the high-frequency instability induced by Local Transmitting Boundary. So the explicit formula is an ideal integration formula for solving the earthquake responses of large-scale structure and complex site.The objective of this dissertation is to further study characteristics of the explicit integration formula in order to make good use of the formula. Trough theoretical studies and numerical experiments, the following problems are analyzed, and some applicable results are obtained.1. The numerical dissipation of this explicit integration formulaThe relationship between frequency, damping and algorithmic dissipation is studied by using this explicit integration formula in solving dynamic equation of single-degree of freedom. Besides, the influences of the algorithmic dissipation on numerical computation are showed by numerical experiments. Research results show that: a) the numerical dissipation of this explicit integration formula is stronger in higher modes, the larger the real damping is, this phenomenon is moreobvious; b) There is a cut-off frequency ω0 when this integration formula is applied to solveSDF dynamic problems under computation stability condition, if frequency is larger than ω0, thesolution become oscillation, and the kind of oscillation is different to diverse damping and frequency.2. The application of this explicit integration formula in wave motion simulation of a one-dimensional discrete finite element modelIn this dissertation, the effect of this integration formula on wave propagation in discrete finite element model is analyzed by studying one-dimensional finite element simulation of wave motion...