Interval Fuzzy Random Finite Element Reliability Analysis Of Structures

There exists much uncertainty in real-life engineering structures. In order to build rational reliability analysis models, one should well understand all kinds of uncertainties. Probability models are the most widely used ones, but it needs large samples to determine their distributions. Furthermore, probabilistic models can only considers randomness, without consideration of other uncertainties, such as fuzziness, incompleteness, etc. Therefore, some generalized reliability models considering all kinds of uncertainties should be investigated to satisfy practical needs in engineering. In addition, there is a need to realize generalized reliability analysis of engineering structures based on existing finite element analysis platforms, to solve the problems of safety analysis and risk evaluation of complex engineering structures in real life.In this thesis, the object-oriented finite element analysis toolbox OpenFEM for MATLAB as well as the large-scale commercial FEM software ANSYS are chosen as computation platforms. Three cases of complex uncertainty for basic variables in structural reliability analysis are considered, namely, interval variables of distribution parameters of probability models, fuzzy variables of distribution parameters of probability models, and fuzzy random variables of basic variables. Two computational reliability methods, i.e., Monte Carlo Simulation (MCS), and First Order Reliability Method (FORM), are implemented and improved to solve the generalized reliability problems under the above uncertainty cases, corresponding to only-randomness and fuzzy-randomness in limit states, respectively. The existing finite element reliability methods (FERM) only considering randomness are then extended to interval fuzzy random FERMs. The main contents are as follows:(1) The interval finite element reliability method in the case of interval variables of distribution parameters of probability models is investigated. The existing interval MCS method without considering the fuzziness is improved to consider the fuzziness in limit states of structures. Combining interval analysis and FORM, a hybrid interval FORM is proposed. The intervals of failure probabilities of truss and frame structures corresponding to only-randomness and fuzzy-randomness are analyzed.(2) The interval finite element reliability method in the case of fuzzy variables of distribution parameters of probability models is studied. Use of the proposed interval MCS and interval FORM is made to calculate the possibility distributions of failure probabilities of truss structures corresponding to only-randomness and fuzzy-randomness respectively.(3) A generalized reliability analysis model with fuzzy random basic variables is built up, a new fuzzy FORM with equivalent random transformation of fuzzy random variables is put forward. Using MCS and the proposed fuzzy FORM, the fuzzy random reliabilities of truss structures corresponding to only-randomness and fuzzy-randomness are analyzed respectively.