Linus Andersson presenterar sin licentiatavhandling
Reduced order modeling in structural dynamics - Consideration of local nonlinearities
A structural design process may include various load cases for which a sufficient load-bearing capacity must be demonstrated. In addition to static load cases, a verification of dynamic loads, e.g. accidental loads such as blast and impact loading, may be required. To this end, the response may be estimated using a computational model representing an idealized structure. Particularly in the conceptual design phase, a time-efficient and straightforward modeling approach can be of great utility, allowing for an interactive design process where alternative designs may be tested. Furthermore, a dynamic response analysis often requires some form of time (or frequency) discretization and can therefore become computationally expensive compared to the corresponding static analysis. The balance between performance and accuracy as well as the purpose, i.e. the output quantities of interest, are thus important aspects in a dynamic response analysis.
A structural dynamics analysis typically requires a model being accurate as well as computationally efficient. The model accuracy is particularly important in a verification of structures characterized by brittle failure modes, i.e. that do not deform plastically before failure. Furthermore, to avoid a too conservative design and to ensure sufficient accuracy, it can be necessary to consider the nonlinear response of a structure, e.g. due to contact interactions or nonlinear material behavior. However, a nonlinear structural dynamic problem often requires computationally expensive solution methods. Consequently, there is a need for modeling strategies that enable time-efficient, accurate analyses and a straightforward modeling approach, appropriate in a structural design process. To achieve this, a reduced order model can be established to provide an accurate prediction of important output quantities.
Dynamic substructuring turns out to be an important aspect in the process of developing reduced order models. By subdivision of the structure into substructures, dynamic substructuring can be employed to effectively adjust the level of accuracy for different parts of the structure. For example, substructures that remain linear elastic can typically be modeled using mode-superposition methods whereas substructures which exhibit a nonlinear behavior can be represented by a refined submodel.
In the dissertation, strategies for reduced order modeling are investigated on the basis of structural engineering applications within two different areas, namely concrete structures subjected to blast loading and glass structures subjected to soft-body impact. Interestingly, however, some of the challenges with regard to the structural dynamics problems are similar. In particular, the response of higher order modes may be of importance and, moreover, an accurate representation of the structural behavior may necessitate a model considering local nonlinearities.
By means of dynamic substructuring, computationally efficient analysis techniques are developed for evaluating concrete structures subjected to blast loading, appropriate for use in a structural design process. In particular, a comparison to commonly used modeling strategies, using equivalent single-degree-of-freedom systems, suggests that the developed models provide an increased accuracy of the shear force. Brittle failure modes such as shear failure are typically critical for concrete structures subjected to blast loading.
Furthermore, reduced order models are established for verification of glass panels subjected to soft-body impact. In particular, a non-linear viscous single-degree-of-freedom system is proposed for reduced modeling of the standardized EN 12600 impactor. Further, the response of higher order modes is considered using a set of load-dependent mode shapes. The developed models are validated by experimental tests of impact on glass panels.
Finally, a review of various reduced order modeling techniques is presented which, in a broader perspective, provide a basis for developing reduced order models in various structural engineering applications.
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Docent Andreas Linderholt, Linnéuniversitetet, Växjö.
Professor Ola Dahlblom, Avd f Byggnadsmekanik LTH.
Professor Kent Persson har varit huvudhandledare och TeknD Peter Persson samt Professor Per-Erik Austrell har varit biträdande handledare, samtliga Avd f byggnadsmekanik, LTH.