Research On Analysis Methods Of Uncertain Structures

A large number of errors and uncertainties exist in the actual structures, and these uncertain factors should be considered in structural analysis. There are mainly four models to deal with uncertainty, which are probability model, fuzzy model, unascertained model and convex model or interval model. Probability model, unascertained model and interval model are discussed in this paper. Based on these models, some researches on the theories and methods of the static response analysis, the dynamic characteristic analysis and the dynamic response analysis for uncertain structures are made respectively. The main research works can be described as follows.1,The static response analysis for random plate-beam composite structures.Considering the randomness of the physical parameters and the loads applied simultaneously, the structural stiffness matrix and the load vector of random plate-beam composite structures are constructed. Then, the static finite element equations of the structure can be built. The numeric characteristics of the structural displacement response and stress response are developed using the random factor method and the algebra synthesis method. The advantage of this method is that the effect of the randomness of one of the structural parameters on the randomness of the structural static response can be reflected expediently and objectively.2,The dynamic analysis for random plate-beam composite structures.The problems of dynamic characteristic analysis and dynamic responses analysis based on probability model for the plate-beam composite structures with random parameters are studied. Firstly, considering the randomness of physical parameters, the numerical characteristics of the structural random dynamic characteristic are obtained by means of the algebra synthesis method from the Rayleigh's quotient of structural vibration. Secondly, considering the randomness of physical parameters, damping and loads respectively or simultaneously, the computational expressions of the numerical characteristic of the structural dynamic response are developed by using the random variable's moment function method and the mode summation method.3,The static response analysis for unascertained structures.The unascertained analysis method is introduced into the analysis of uncertain structures. Considering the uncertainties of the structural physical parameters, geometrical dimensions and the loads simultaneously, the finite element analysis model of truss structure is built. And an uncertain structure analysis method based on the unascertained factor method is given. By applying the mathematics expression of unascertained factor and the arithmetic operation rules of unascertained rational numbers, the computational expressions of the structural displacement response and the element stress response are developed. The elaborate response results can be obtained by this method.4,The dynamic characteristic analysis for unascertained structures.The unascertained analysis method is introduced into the dynamic characteristic analysis of uncertain structures. Considering the uncertainties of the structural physical parameters and the geometrical dimensions simultaneously, the unascertained model for dynamic characteristic analysis of uncertain structure is developed from the Rayleigh's quotient of structural vibration. And a structure dynamic characteristic analysis method based on the unascertained factor method is given. By the mathematics expression of unascertained factor and the arithmetic operation rules of unascertained rational numbers, the computational expressions of the natural frequencies are developed. The rationality and validity of the theory and method presented in this paper are inspected by an antenna example, from which the possible values and the faith degrees of the unascertained structure characteristics are obtained.5,Unascertained method for the reliability allocation.The unascertained method is popularized for the reliability allocation of structure system. For the shortage of the reliability datum in the initial stages of the design of a spaceborne antenna deployment mechanism, unascertained method for system reliability allocation is proposed. This method is based on the weight allocation method. Through the introduction of the unascertained information into the matrix of weight coefficients, the unascertained model for the reliability allocation of spaceborne antenna deployment mechanism is built. By using the arithmetic operation rules of unascertained rational number, the expression of unascertained weight coefficient is derived. Finally, the reliability allocation of a spaceborne antenna deployment mechanism is given as an example. The possible values and the faith degrees of the system are obtained, which verify the rationality and feasibility of the presented method.6,The static response analysis based on interval model.By representing the uncertain parameters as interval numbers, the governed equations of the structure are obtained by means of the interval finite element method. The interval finite element governed equations are solved by the Monte Carlo numerical simulation method. And an improved Monte Carlo numerical simulation method is presented for improving the performance of common Monte Carlo method. The computation steps of improved Monte Carlo method is given too. The improved Monte Carlo method for solving the interval equations is easy to imply. High accuracy solutions can be obtained by this method. And the overestimation which is the major drawback of interval analysis is overcome.7,The dynamic analysis based on interval model.By representing the uncertain parameters as interval numbers, the interval dynamic characteristic equations and the dynamic governed equations of the structure are built by means of the interval finite element method. The interval finite element governed equations are solved by the improved Monte Carlo method. And the dynamic characteristics, the dynamic displace responses and the dynamic stress responses are obtained. Easier implement and higher accuracy solutions can be obtained by the improved Monte Carlo method.8,Interval analysis method for uncertain structures based on the blind number theory.The problems of static response analysis and dynamic analysis based on the blind number theory for uncertain truss structures are studied. Firstly, considering the uncertainties of the structural physical parameters, geometrical dimensions and the loads simultaneously, the interval finite element governed equations of the structure are developed. Based on the common interval analysis method and the expression of blind number, the blind number factor method is proposed. By this method the governed equations can be solved. And the possible intervals and the faith degrees of displacement responses and stress responses are obtained. Secondly, considering the uncertainties of the structural physical parameters and geometrical dimensions at the same time, the dynamic characteristic analysis model for uncertain structures based on the blind number theory is constructed. The possible intervals and the faith degrees of nature frequencies are gotten by means of the blind number factor method.The theories presented in the paper are important and meaningful in the following aspects: perfecting the analysis model for uncertain structures, enhancing the solution ability and the computation precision of the FEM for uncertain structures, and improving the application of the uncertain analysis methods in practical engineering.