Reduced Order Modeling and Substructuring : Applications in Nonlinear Structural Dynamics

Sammanfattning: A structural design process typically involves various load cases for which a sufficient load-bearing capacity must be demonstrated. In addition to static load cases, a verification of dynamic loads, such as blast and impact loading, may be required. To this end, the response can be estimated using computational models representing an idealized structure, often formulated using the finite element method. In contrast to static analyses, a dynamic response analysis generally requires some form of time (or frequency) discretization. Furthermore, to properly capture the structural behavior, it can be necessary to consider nonlinear effects, e.g., due to contact conditions, nonlinear material behaviors, or geometrically nonlinear effects. The repeated solution in time of large nonlinear finite element models can be computationally expensive and time-consuming. Consequently, there is a need for computationally efficient modeling approaches, allowing for an interactive design process where alternative designs may be tested in a time-efficient manner.By generating a reduced order model, the aim is to reduce the system size while maintaining sufficient accuracy of important output quantities. Hence, the computational cost can be reduced by analyzing a smaller, approximate system. For continuous structural dynamics problems discretized using the finite element method, reduced order models can be obtained by introducing a reduction basis. More specifically, the response is approximated using a set of time-independent displacement fields, referred to as mode shapes, which constitute the basis vectors of the modal basis. This approach is well-established and frequently used within linear structural dynamics. In the context of nonlinear structural dynamics, modal methods for reduced order modeling have gained more prominence during the last decades and is still an active area of research.In the dissertation, strategies for nonlinear reduced order modeling are developed on the basis of structural engineering applications within two different areas; namely, concerning concrete structures subjected to blast loading and glass structures subjected to impact loading. Some of the challenges with regard to structural dynamics modeling are similar. In particular, brittle failure modes are often critical, why the response of higher order modes can be of particular importance. Moreover, an accurate representation of the structural behavior typically necessitates models considering nonlinear behaviors. More specifically, the dynamic problems involve localized nonlinearities in the form of contact conditions and joints, as well as geometric nonlinearity which, in contrast, is a distributed nonlinearity where degrees of freedoms throughout the structure are nonlinearly coupled.Impact loading is a fundamental load case in design of glazed barriers, such as full-height facades and balustrades, which often governs the design. In this work, modeling strategies were developed for predicting the pre-failure elastic response of flat glass panels subjected to a standardized impactor, which represent a human body falling towards the glass panel. The response of glass panels, having a small thickness compared to the span width, are typically characterized by bending-stretching coupling effects. To consider these effects, which result in a geometrically nonlinear behavior, reduction bases were generated using bending modes and the associated static modal derivatives, corresponding to the second order terms in a Taylor’s expansion of the quasi-static displacement field. Moreover, approximate techniques for modeling contact were proposed, and a nonlinear viscous single-degree-of-freedom model was developed for reduced modeling of the impacting body. The response was evaluated based on experimental data and detailed finite element models. For the studied load cases, the proposed model was shown to predict important output quantities, such as the glass principal stresses, with high accuracy.Furthermore, computationally efficient analysis techniques were developed for analysis of concrete structures subjected to blast loading. Specifically, reduced models including pre-defined plastic joints were developed by means of dynamic substructuring. A comparison to commonly used modeling strategies, which uses equivalent single-degree-of-freedom systems, suggests that the developed models provide a significantly improved accuracy of shear forces. This can be critical in a verification of brittle failure modes, such as diagonal and direct shear failure.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 dynamics applications.