Advanced combinatorial methods for solving the governing equations of linear static interval finite element method

The static governing equations of interval finite element method (FEM) are always transformed into interval equations to be solved. But, in fact, they are not equivalent. The mechanical background of the finite element analysis of uncertain structures are taken into account, and starting directly from the uncertainties of the basic parameters, two combinatorial procedures for solving the governing equations of linear static interval FEM are presented. In these procedures, the boundary combination of basic interval parameters is used for solving the interval equations of the interval analysis of structures. The presented procedures may have a high accuracy and low computational burden, and are not restricted by the variation ranges of the basic parameters. Two numerical examples have illustrated the applicability and the effectiveness of the proposed procedures.