A Study On Appication Of Hybrid Finite Element In Stochastic Analysis Of Structures

Stochastic structural analysis and reliability analysis are the analysis of structure in consideration of the uncertainty of structural parameters, these procedures is becoming increasingly important in structural design and structural assessment. This is why it is essential to find a better numerical computation scheme. At the present stage, the most commonly used method is stochastic finite element method(SFEM) which is based on non-conforming element. In order to improve the quality of SFEM, the solution presented in this dissertation is to use the hybrid stress element instead of displacement element, because of the advantage of hybrid element in the calculation accuracy and the material heterogeneous problem. Then, the calculation accuracy of the reliability analysis will be improved by the application of new stochastic analysis method in reliability analysis.In this paper, we will take the stochastic problem with variable elastic modulus as an example to illustrate this method.Firstly, the basic concepts and the development of hybrid stress element are briefly introduced, and the effectiveness of the method in the are of deterministic analysis is validated by numerical examples.Secondly, after using the Karhunen-Loeve expansion method to discrete the random field, the elastic modules in the formulation has been replaced by random variable. Then, the mean and standard deviation of structural responses are derived by using the first order perturbation. This new methods transform the random process into a deterministic problem like the other methods, considering the advantage of hybrid element in the deterministic problem, the new stochastic finite element method which is based on hybrid stress element is a better scheme than the SFEM which is based on displacement element. Numerical examples are given to show the accuracy and efficiency of the proposed method.Thirdly, the derivative of the structural responses with respect to random variable which was derived in SFEM is utilized for reliability analysis with the advanced first-order-second-moment(AFOSM) method. The reliability analysis process can be regarded as post-processing of the derivative.Since we have verified the advantages in stochastic analysis, in a similar way, the application of hybrid stress element will improve the calculation accuracy of the reliability analysis. The accuracy and efficiency are investigated by numerical examples.The work in this dissertation shows that the SFEM which is based on hybrid element have a good precision in stochastic analysis and reliability analysis. It also shows the advantages of hybrid element in deterministic problem with variable elastic modulus.