Perturbation finite element method of structural analysis under fuzzy environments

A preliminary analysis of the perturbation fuzzy finite element was provided by Yang et al. (Appl. Math. Mech. 20(7) (1999) 795). In this paper, we provide a detailed analysis of the perturbation fuzzy finite element method based on variational principle. Firstly, on the basis of the second-order perturbation principle of small parameter, the fuzzy functional of total potential energy and the definite perturbation expansions are proposed. Secondly, definite recursion equation of fuzzy variational principle is deduced and fuzzy finite element recursion functional is presented based on fuzzy variational principle. Thirdly, the proposed approach is compared with the conventional fuzzy finite element method. Finally, a numerical example is given to illustrate the method.