The problems of interest span a wide spectrum, ranging from civil structures (buildings & bridges) to aerospace structures (missiles & re-entry vehicles). Computational models arising from these diverse arenas share the common traits that they are large in size, often consisting of 103 to 108 degrees-of-freedom, and possess uncertainties and nonlinearities. In addition, one desires, using these large computational models, to perform response predictions; to design individual components in the system; to make decisions on optimal and robust strategies for controlling the dynamics and corresponding responses; and to monitor and identify dynamic characteristics of the system. However due to the model's size, the computational expense of performing the desired iterative analyses is high if not prohibitive.
Our research approach results from the observation that the uncertainties and/or nonlinearities in many of these extremely large structural models arise from a small number of local nonlinear or uncertain features, whereas the remainder of the model is linear and deterministic. These features may occur, for example, due to uncertainties in the properties of structural members, non-linear behavior of plastic hinge regions in beams and columns, or time-varying properties due to active, semiactive or passive control systems. By exploiting this locality, exact model reduction methodologies can be developed. For linear structural systems with local uncertain members, computational algorithms have been successfully developed to efficiently compute their modal characteristics (IJNME, 2009), their frequency response to deterministic excitations (ASCE JEM, 2011) and their spectral response (PSD) to stationary random excitations (PEM, 2010) - with significant reduction in computation. Similarly, an algorithm for the transient response of nonlinear dynamical systems with local nonlinear and/or uncertain features has also been formulated (PEM, 2011). Application of these methods to a moderately sized finite element model of a building yields gains in computational efficiency of two to three orders of magnitude. Finally, the efficacy of this notion of locality is not restricted to purely computational models. In a collaborative effort (SM&S, 2011) with Prof. Richard Christenson at the University of Connecticut, a new real-time hybrid testing method, using these theoretical developments, was developed and experimentally verified to conduct real-time hybrid testing of semiactive control devices. This will allow for higher fidelity models, with many thousands of degrees of freedom, to be incorporated in the experimental validation of semi-active control for complex civil structures.
The Group has developed key extensions to this work for computationally efficient design optimization, uncertainty analysis and structural control design. (i) Locality can be exploited to efficiently compute not only responses, in both the time and frequency domains, but also sensitivities of these responses to parameters in the nonlinearities. (ii) The approach has been adapted to make efficient the large-scale parameter studies often required in semi-active structural control design. (iii) The method has also been adapted to exploit the massively-parallel computation available with graphics processing units (GPUs). These results will be forthcoming.
The research results will enable engineers to employ computational models of much greater fidelity to: (1) assess uncertainty in key system component response; (2) 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; and (3) facilitate more efficient characterization of the impacts of structural system degradation. The Group would also like to acknowledge the partial support of this work by the National Science Foundation through CMMI-1100528.
1. Gaurav, S.F. Wojtkiewicz, and E.A. Johnson
(2011). "Efficient Uncertainty Quantification of
Dynamical Systems with Local Nonlinearities
and Uncertainties," Probabilistic Engineering
2. Wojtkiewicz, S.F., Gaurav, and Q. I. Odes (2011).
"Efficient Frequency Response of Locally
Uncertain Linear Structural Systems," ASCE
Journal of Engineering Mechanics, 137(2): 147-
3. Gaurav and S.F. Wojtkiewicz (2011). "Use of GPU
Computing for Uncertainty Quantification in
Computational Mechanics: A Case Study,"
Scientific Programming, 19(4):199-212.
4. Kim, S.J., R.E. Christenson, S.F. Wojtkiewicz, and
E.A. Johnson. (2011). "Real-time Hybrid
Simulation using the Convolution Integral
Method," Smart Materials and Structures,
5. Gaurav and S.F. Wojtkiewicz, (2010). "Efficient
Spectral Response of Locally Uncertain Linear
Systems," Probabilistic Engineering Mechanics,
6. Wojtkiewicz, S.F., and Gaurav (2009). "Efficient
Modal Analysis of Structures with Local Stiffness
Uncertainties," International Journal for
Numerical Methods in Engineering, 80:1007-