Generalized reliability analysis of structues based on interval finite element

Abstract

Relative to the special structure reliability theory only considering randomness, the advanced theory is called generalized reliability which considers randomness, fuzziness and unascertainty at the same time. This theory was first proposed by Wang GuangYuan academician in 1980s. In this thesis, some research results of the team of authors are introduced. Fuzziness is considered by the fuzzy mathematics and unascertainty is reckoned with the interval mathematics. First, some basic conceptions of interval math and interval finite element are introduced. Then generalized reliability analysis methods of three kinds of uncertainty conditions are discussed with the tool of interval finite element. In the first condition, both randomness and unascertainty are considered and the parameters of the random variables are interval variables. The second condition is that randomness and fuzziness are separated. The basic variables are random and the failure criterion is fuzzy. Randomness and fuzziness are coupling in the third condition. The parameters of the random variables are fuzzy numbers to reflect fuzziness. Finally, authors propose and develop the generalized reliability analysis methods of this three cases using the interval Monte Carlo Simulation (IntMCS) and the interval First Order Reliability Method (IntFORM). By means of a plane truss example, the applicability and effectiveness of these methods are shown. After a series of research, some conclusions can be summarized. The IntFORM proposed in this thesis has enough computational accuracy and more computational efficiency than IntMCS. Therefore, this method can be used in the reliability analysis of large-scale structures.