On Problems Related To Nonlinear Transient Dynamic Analysis

Abstract eng:
One of the key objectives of simulation is the prediction of the response of real structures to real loading. As every loading happens in time and every structure exhibits a more or less nonlinear behaviour, all real problems are nonlinear and transient. Fortunately, in many cases, simplifications like static or linear models are acceptable. But in many cases, full nonlinear transient studies including the increasing modelling uncertainty have to be performed. Both the handling of the nonlinearities and the time integration inhibit possible weaknesses which may cause simulation results which are poor with regard to their capability to reproduce phenomena observed. While the nonlinearities may be handled by an accepted model of the corresponding physical phenomena, the time integration produces some additional difficulties. There must be no doubt that very small time steps yield acceptable quality of the structural response. But for problems covering longer periods of time, the total number of time steps and the corresponding computation time may become too large to handle the problem within adequate cost and time. Typical examples are transient studies where higher Eigen frequencies play an important role for the total deformation of the structure under consideration. In many cases, numerical integration appears to be successful, while physical instabilities are cancelled out by numerical damping, e.g. when using implicit integration schemes like some variants of the generalized α-method [1, 2]. A special class of difficulties is encountered when dealing with inadequately posed questions, e.g. simulations where bifurcations or other non-unique responses may be observed. In many cases, the numerical tools propose time histories that seem to be representative for the problem posed. Furthermore, a broad list of numerical stabilization proposals helps to overcome critical points in the loading history. In those cases, one of the possible branches of the solution is preferred without further discussion of the importance of the other branches. Often, users of commercial codes accept default proposals of the systems and are not aware of their influences on the results. Especially in the case of explicit time integration, small adjustments like modification of the density to increase the allowable time steps may cause surprising effects. To come up with reliable results in nonlinear transient problems, a deep understanding of the physics of the problem is necessary. Furthermore, the possible effects of the different numerical options have to be studied carefully. A clear and reproducible documentation of the uncertainties should be performed. In the case of bifurcations, all branches that may be significant to the study have to be followed and understandable decisions have to be made regarding which of the different solutions should be considered.

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