Uncertainty modeling for nonlinear dynamic systems--loadings applied in time domain

Enormous amount of damages to structures caused by recent major seismic events indicate shortcomings or incompleteness in their design. Some of the major weaknesses in current practices include the inability to incorporate major sources of uncertainty in the formulation, realistic structural behavior leading to failure, and most importantly predicting the exact design earthquake time history expected during the lifetime of a structure for a specific site. To address excessive economic losses, the performance-based seismic design (PBSD) concept is being advocated in the U.S., particularly for steel structures. This is essentially an advanced risk-based design concept. The author’ steam proposed several novel concepts to estimate the underlying risk considering major sources of nonlinearity and uncertainty in the past, including the stochastic finite element concept. However, the risk analysis procedure for realistic nonlinear structural systems excited by seismic loadings in the time domain, required for the most sophisticated deterministic analysis, is not available at present. To make the design more seismic load tolerant, multiple earthquake time histories need to be considered to incorporate uncertainty in the frequency content. If one decides to use simulations to extract the reliability information, it may not be possible; it may require several years of continuous running of a computer. The author’s team proposed several alternatives to simulations. Several related topics to make structures more seismic damage tolerant are presented in this paper.