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| A reliable approach to compute the static response of uncertain structural system |
| Revised:February 28, 2002 |
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| DOI：10.7511/jslx20036127 |
| KeyWord:uncertainty,interval analysis,interval mathematics,global optimization,genetic algorithm |
| Wang Denggang~ |
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| Abstract: |
| Uncertainties widely exist in engineering structural analysis and design problems and cannot be just neglected. The probabilistic method, the fuzzy method and the interval method are the three major approaches to model uncertainties at present. Representing the uncertain structural material parameters, uncertain structural geometric parameters and the uncertain loading conditions as the interval numbers, the structural static response accurately by solving linear interval equations. Overestimation is a major drawback in interval computation. Thus, a reliable computation approach was proposed to overcome it in the paper. The presented approach is based on the inclusion monotone property of interval mathematics and the physical/real meaning expressed by the interval function. The interval function and the linear interval equations were solved by solving the corresponding optimization problems to determine the endpoints/bounds of every interval element of the solutions of the problem. Moreover, an intellective algorithm named as real-code genetic algorithm was used to locate the global optima of these optimization problems. Some mathematical and structural examples were used to examine the efficiency of the approach first. Then, this approach was combined with finite element method to determine the response interval of uncertain structural system. A very sharp enclosure for the solution set, due to material, geometric and loading uncertainty in structural analysis problems, was obtained. |
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