DIRECT INTEGRATION IN MODELS WITH TRANSMITTING BOUNDARIES

Abstract

The dynamic analysis of soil structure systems is often carried out using direct method and direct integration of equations of motion in the time domain. For such ,3n analy,ls -In artificial boundary is introduced for the soil region, which is truly unbounded. If this artificial boundary is assumed to be elementary, then the 'soil structure system will behave like a closed box and no energy will be transmitted out. Therefore, it is essential that the artificial boundary has transmitting capabilities so that the unbounded nature of the soil can be properly represented. In this study various transmitting boundaries available in the literature are discussed. The Generalised Newmark algorithm, that can be employed explicit as well as implicit procedures is also discussed. The efficacy of a popular, transmitting boundary viz. a viscous dashpot with specific damping4.coe.fficlent is studied for one dimensional wave propagation problem. It is seen that the effectiveness of such a transmitting boundary is influenced by discretization, choice of the direct integration procedure and the choice of the time step. It is further observed that if the discretization and the choice of the algorithm is proper locating the artificial boundary a large distances for one dimensional problems is not particularly advantageous