Date of Award
Doctor of Philosophy (PhD)
Committee Member 1
Shirley J. Dyke
Committee Member 2
Michael E. Kreger
Committee Member 3
Numerical simulation of large-scale problems in structural dynamics, such as structures subject to extreme loads, can provide useful insights into structural behavior while minimizing the need for expensive experimental testing for the same. These types of problems are highly non-linear and usually involve material damage, large deformations and sometimes even collapse of structures. Conventionally, frame structures have been modeled using beam-frame finite elements in almost all structural analysis software currently being used by researchers and the industry. However, there are certain limitations associated with this modeling approach. This research focuses on two issues, in particular, of modeling frame structures undergoing large deformations and rotations when subject to extreme loads such as high intensity earthquakes.
One of the issues with using beam-frame models is that the theoretical formulation and numerical implementation of such models are rather complicated and are not well understood by the average engineer using such computer programs. The complications arise primarily due the non-additive nature of three dimensional rotational degrees of freedom, especially under large rotations. Further, ensuring that the time integration schemes used for such models provide stable and accurate solutions is still an active and challenging area of research. To address this issue, a reduced order model that idealizes a frame structure as a network of rotational and extensional springs is developed. This formulation eliminates all the rotational degrees of freedom in the system by expressing the force-displacement and moment-rotation relationships only in terms of nodal coordinates. This not only simplifies the formulation, making it similar in complexity to a network of truss elements, but also avoids the numerous implementational hurdles associated with large three dimensional rotations. Several numerical examples are presented to verify and validate the performance of this approach against conventional beam-frame elements.
Existing models that attempt to capture the non-linear behavior of structures undergoing large deformations and damage, which often occurs across multiple scales of space and time, are either limited in the level of fidelity they offer or have an extremely high computational cost associated with them. A computationally advantageous way of approaching such problems is to decompose the structural domain into two regions, one comprising most structural elements where beam-frame elements can be used, and the other consisting of joint and connection regions where more detailed continuum elements can be used as needed. This allows one to model the critical structural components with great fidelity, while still using beam elements for the rest of the model to keep the total computational cost in check. An essential ingredient for this approach is the formulation of a geometrically consistent coupling of beams and continuum elements, especially in the presence of large deformations and large rotations. In addition to spatial coupling of beam and continuum elements, a multi-time-step method is also formulated to allow the beam and continuum elements to be simulated at different time scales. This further adds to the computational efficiency of this approach. Numerical characteristics of such coupled models are verified with a variety of static and dynamic benchmark problems.
Liu, Hui, "Modeling of frame structures undergoing large deformations and large rotations" (2016). Open Access Dissertations. 798.