Analysis Of Structures (Mechanisms) With Interval Or Unascertained Parameters

Firstly, structures with interval parameters, random-interval parameters or unascertained parameters are taken as research objects in this paper. Structural static responses, dynamic characteristics, dynamic responses and non-probability reliability index are derived under the conditions that physical parameters of materials, structural geometric dimensions and applied loads are all interval, random-interval or unascertained variables. Secondly, based on the engineering background of national 863 project, reliability computation, prediction and analysis on deployment mechanism system of satellite antenna are derived by means of unascertained theory. The main research works can be described as follows:1. The static analysis of interval truss structures.By representing the uncertain parameters as interval numbers, the governed equations of the structural system are obtained by means of the finite element method. Some solution methods for these equations are discussed and affine arithmetic polynomial evaluation method plus recursive derivative information is proposed. In this method, the independent uncertain parameters are transferred to affine forms, and the linear interval equations are changed to the corresponding certain ones. Then the bounds of every interval solution components are determined by searching for the maximums and the minimums.2. The study on dynamic characteristic and dynamic responses of interval truss structures.Not only considering the interval characteristics of structural physical parameters and geometric dimension, but also considering interval characteristics of applied load simultaneously, uncertainty of the MDOF structural dynamic response is studied. By describing the interval parameters of uncertain structure with affine forms, the interval structural dynamic equation is researched, and an improved affine arithmetic based on interval division is presented, where correlations between the interval elements in eigenvalue and responses equations are considered, independent uncertain parameters are transformed to affine forms, and the solution of eigenvalue and response equations are transformed into the corresponding certain ones. With general affine arithmetic, the eigenvalue of each order and response bounds are determined by searching for the maximum and minimum in the solutions. Some numerical examples were provided to illustrate the validity and feasibility of the present method.3. Non-probabilistic reliability index of bar structures with interval parameters based on modified affine arithmetic.By representing the uncertain parameters as interval numbers, the reliability index equations of bar structures are obtained. A modified matrix affine arithmetic polynomial evaluation method plus recursive derivative information is proposed in this paper, which keeps all powers of noise symbols without approximation. Based on the nature that affine forms and intervals variables can transform each other, affine forms of bounded uncertain variables and modified affine arithmetic including derivative information for univariate interval polynomial evaluation are introduced into modeling and calculating non-probabilistic reliability index. An extended beam example and a ten-bar truss structure example are provided to illustrate the validity and feasibility of the presented procedures.4. Interval method with faith degree constraints for structures analysis.The finite element analysis model of uncertain truss structures is built, in which the structural physical parameters, geometrical dimensions and the loads are all considered as unascertained variables. And a structural analysis method based on the interval factor method with faith degree constraint is given. The arithmetic operation rules of interval analysis with faith degree constraint are defined. By the mathematics expression of interval factor, the computational expressions of structural static responses, dynamic eigenvalue and dynamic responses are developed.5. Dynamic eigenvalues analysis of structures with interval parameters based on probabilistic theory.By describing the interval parameters of uncertain structure with random variables, a generalized eigenvalues interval equation was researched, and a simple arithmetic was presented. The interval variables were supposed to be rectangle distribution with maximum entropy in allowable range, and random variables obeyed uniform distribution in definition region on the assumption that they were independent each other. The solution of interval eigenvalues equations are tackled by using the probabilistic theory, then the random factor method is applied to obtain the bounds of eigenvalues. For comparisons, the interval variables are also supposed to be random normal distribution and the corresponding eigenvalues ranges are obtained. Finally an engineering application was applied to confirm the feasibility and validity of this approach.6. Finite element and reliability analyses for antenna structures with the mixture of random and interval variables.A model for finite element and reliability analyses for antenna structures with random parameters under interval loads was constructed, a new method of finite element analysis for dealing with structural uncertainty factors was presented, and the structural probability descriptions in the cases of preserved-precision and preserved-intensity were given. The stochastic property of physical parameters and geometry dimensions and the interval property of wind loads applied on antenna structures were considered simultaneously. Firstly the stochastic variables were fixed to obtain the ranges of structural displacement and stress by using the interval factor method, and then the random distribution ranges of structural responses for any points in the interval were gained based on the random factor method. The computational expressions for the numerical characteristic of antenna reflector responses including displacements and structural element stresses were constructed; thereby the reliability indexes of the structural responses were obtained. Finally, the rationality and the feasibility of the method were confirmed by the analysis of an antenna structure with an 8-meter caliber.7. Reliability analysis for antenna deployment mechanism based on unascertained theory.The deployment principium of a large hoop-truss satellite antenna was studied and the mechanical analysis model and the unascertained reliability model of its deployment mechanism were presented. Synthetically considering the effect of dimension errors and the space environment factors, we treat the mechanism movement as a function of some unascertained rational numbers, and derive the reliability formula by using computational theorem of unascertained rational numbers. The movement reliability of the mechanism of a large satellite antenna in the whole spreading process is predicted. Compared to the mature random method, the proposed method can obtain reliability result of safer and higher faith degree in the case of inadequate data or insufficient information; moreover, it is simple and easy to apply.8. Static and dynamic eigenvalue analysis for beam-plates composite structures based on unascertained theory.Random method doesn't suit the case of small sample. To overcome this limitation, the objective unascertained information was made full use of, and the static finite element and dynamic characteristic analysis models of space beam-plate composite structure were built, in which the structural physical parameters and the applied loads were all considered as unascertained variables. And a structure analysis method based on the unascertained factor method was given. By the mathematics expression of unascertained factor and the arithmetic operation rules of unascertained rational numbers, the computational expressions of the structural displacement response, the element stress response and dynamic eigenvalue are developed. At last, an example is given, in which the possible values and faith degrees of the unascertained structure static responses and natural frequency are obtained. The rationality and validity of the presented method are demonstrated.