The main goal of this research project is to study and develop validated approaches which can accurately and efficiently determine the responses of mostly linear but locally nonlinear and uncertain structural systems. The structural systems in civil, mechanical and aerospace engineering often encounter nonlinearities that are localized. For designs, control, and identification and health monitoring, such locally nonlinear systems are, however, numerically analyzed as if the whole systems were nonlinear. The numerical analyses of such nonlinear systems can be computationally demanding. To accomplish this goal, a novel model reduction strategy utilizing the Volterra convolution integrals will be examined to include time-varying local features and feedback characteristics, and the use of emerging computing architectures such as Graphics Processing Units will be investigated for efficient data processing. The computational approaches developed in the research will be validated through applications to a series of germane benchmark problems involving dynamic analyses, identification and control of base-isolated buildings, bridge with nonlinear bearings, and bridge stay cables.
The research results will enable engineers to efficiently design, identify, and optimize passive and semi-active nonlinear response control devices that are used for the mitigation of the impact of natural hazards. The research will also facilitate more efficient characterization of the impacts of structural system degradation. The project will give advanced training to graduate and undergraduate students at the University of Minnesota and University of Southern California through their involvements in the research project. The internal programs at both institutions will be utilized to recruit students from underrepresented backgrounds to work on this research project. For their wider utilization in future research and practice, the project findings will be disseminated to the broader technical community through demonstration modules developed for formal courses, conference presentations, and journal publications. The research will be integrated in the investigators' ongoing outreach activities involving elementary, middle and high school students to expose them to structural dynamics and engineering design problems involving uncertainty.
The analysis and design of complex structural dynamical systems takes many forms and has numerous challenges. Whether the structural application is the earthquake-driven motion of a building, the rotating cable and drill bit of an oil rig, the collapse of a major bridge and lifeline, or the movement of aircraft wings from in-flight forces, problems in structural dynamics abound. These engineering structures are designed through the use of large computational simulation models which often require hours if not days of time to complete. Many structural engineering analyses amount to asking "What If?" questions. For instance, how does a hospital building perform if it is subjected to an earthquake twice as large as it was designed to withstand. Structural design processes then consider a myriad of mitigation strategies to ensure the safety and reliability of the structural system when faced with a variety of these "What If?" scenarios. To investigate this collection of scenarios, the large computational simulation models must be exercised for each different scenario, thereby amplifying the required computational time from hours to months or even years. Clearly, this duration is not feasible when the engineer must make decisions during the design process; as a result, this computational burden is typically reduced by employing approximations or greatly reducing the number of scenarios considered. The aim of this project was to remove this computational bottleneck for a class of structural systems where the "What If?" questions, and the mitigation strategies considered to ensure structural safety, directly involved only a localized portion of the system that still impacts the response of the rest of the structure. For example, one might consider retrofitting the hospital building with damping mechanisms to isolate the base of the building from the earthquake ground motion; while the addition of this base isolation system will have a profound effect on the response of the entire hospital, the change in the computational model is localized to the area between the base of the hospital and the foundation. The prime outcome of this project has been the creation of a suite of robust, rigorous numerical techniques for response analysis, sensitivity analysis, control design, and uncertainty quantification of structural systems with these local features. These techniques have been demonstrated to produce gains in computational efficiency from 100 to 10,000, reducing analyses that would have required months of computation time to ones performed in a matter of minutes, with no loss in accuracy. Or, alternatively stated, these techniques allow for the consideration of hundreds or even thousands more design scenarios for the same fixed computation time. The approaches developed in this project have been applied for highly-efficient design of conventional and controllable passive dampers to reduce the responses of buildings and bridges to strong winds and earthquakes. Further, similar efficient tools have been utilized to quantify how localized uncertainties or changes in a structure affect its performance, which has application to civil, mechanical and aerospace structures. The project has involved four student researchers— three Ph.D. students, one M.S. student, and one undergraduate (a research assistant, from an underrepresented group, funded through the Northstar STEM Alliance) — who have received mentoring and training in advanced research techniques.
