Efficient Re-Analysis Methodology for Probabilistic Vibration of Large-Scale Structures

It is challenging to perform probabilistic analysis and design of large-scale structures because probabilistic analysis requires repeated finite element analyses of large models and each analysis is expensive. This paper presents a methodology for probabilistic analysis and reliability based design optimization of large scale structures that consists of two re-analysis methods; one for estimating the deterministic vibratory response and another for estimating the probability of the response exceeding a certain level. The deterministic re-analysis method can analyze efficiently large-scale finite element models consisting of tens or hundreds of thousand degrees of freedom and large numbers of design variables that vary in a wide range. The probabilistic re-analysis method calculates very efficiently the system reliability for many probability distributions of the design variables by performing a single Monte Carlo simulation.

The methodology is demonstrated on probabilistic vibration analysis and reliability-based design optimization of a realistic vehicle model. It is shown that computational cost of the proposed re-analysis method for a single reliability analysis is about 1/20^th of the cost of the same analysis using NASTRAN. Moreover, the probabilistic re-analysis approach enables a designer to perform reliability based design optimization of the vehicle at a cost almost equal to that of a single reliability analysis. Without using the probabilistic reanalysis approach, it would be impractical to perform reliability based design optimization of the vehicle.