Risk Estimation of Nonlinear Time Domain Dynamic Analyses of Large Systems

Abstract

A novel concept of multiple deterministic analyses is proposed to design safer and more damage-tolerant structures, particularly when excited by dynamic including seismic loading in time domain. Since the presence of numerous sources of uncertainty cannot be avoided or overlooked, the underlying risk is estimated to compare design alternatives. To generate the implicit performance functions explicitly, the basic response surface method is significantly improved. Then, several surrogate models are proposed. The advanced factorial design and Kriging method are used as the major building blocks. Using these basic schemes, seven alternatives are proposed. Accuracies of these schemes are verified using basic Monte Carlo simulations. After verifying all seven alternatives, the capabilities of the three most desirable schemes are compared using a case study. They correctly identified and correlated damaged states of structural elements in terms of probability of failure using only few hundreds of deterministic analyses. The modified Kriging method appears to be the best technique considering both efficiency and accuracy. Estimating the probability of failure, the post-Northridge seismic design criteria are found to be appropriate. After verifying the proposed method, a Site-Specific seismic safety assessment method for nonlinear structural systems is proposed to generate a suite of ground excitation time histories. The information of risk is used to design a structure more damage-tolerant. The proposed procedure is verified and showcased by estimating risks associated with three buildings designed by professional experts in the Los Angeles area satisfying the post-Northridge design criteria for the overall lateral deflection and inter-story drift. The accuracy of the estimated risk is again verified using the Monte Carlo simulation technique. In all cases, the probabilities of collapse are found to be less than 10% when excited by the risk-targeted maximum considered earthquake ground motion satisfying the intent of the code. The spread in the reliability indexes for each building for both limit states cannot be overlooked, indicating the significance of the frequency contents. The inter story drift is found to be more critical than the overall lateral displacement. The reliability indexes for both limit states are similar only for few cases. The author believes that the proposed methodology is an alternative to the classical random vibration and simulation approaches. The proposed site-specific seismic safety assessment procedure can be used by practicing engineers for routine applications. The proposed reliability methodology is not problem-specific. It is capable of handling systems with different levels of complexity and scalability, and it is robust enough for multi-disciplinary routine applications. In order to show the multi-disciplinary application of the proposed methodology, the probability of failure of lead-free solders in Ball Grid Array 225 surface-mount packaging for a given loading cycle is estimated. The accuracy of the proposed methodology is verified with the help of Monte Carlo simulation. After the verification, probability of failure versus loading cycles profile is calculated. Such a comprehensive study of its lifetime behavior and the corresponding reliability analyses can be useful for sensitive applications.