Finite Element Analysis Based On Interval Method And Application In The Frame

In traditional finite element simulation, the parameters and characteristics of structures are usually specified to be deterministic values. However, under practical engineering situations, some structural parameters are often uncertain, such as the inaccuracy of the measurement, errors in the manufacturing and assembly process, model simplifications and variability on material characteristics etc. For a reliable and reasonable result, some non-deterministic approaches are probably the right answer.Depending on the type and extent of these uncertainties in an engineering structure, three approaches are used for its analysis and design: (a) theory of probability and random processes; (b) fuzzy set; (c) interval analysis. The interval analysis is a new non-probabilistic method. Obviously, It takes an advantage over probabilistic models, since only the bounds of the uncertain parameters are required, not necessarily knowing the probability distributions or membership functions.Based on interval mathematics, interval finite element model is established for static analysis and modal analysis, and then ,static analysis and modal analysis have been done on a ten-bar truss example, and The comparison between the interval method and the Monte Carlo simulation method indicates the proposed interval method is more effective; In addition, a side beam frame model is also established in this paper. Density and elastic Modulus of the material of the frame model are interval parameters. Modal analysis has been done on the frame model, The comparison between the interval method and the Monte Carlo simulation method has also been done. The results obtained provides a theoretical basis for the improvement of structural design of the frame, and has done some preliminary work for the further development of structural vibration equation, estimation on the system response under external force and further study of vibration, fatigue and noises and so on.