Aimed at physical and geometrical uncertainties broadly existed in practical engineering, an effective method for the supremum and infimum of the static response of structures with bounded uncertainties was presented. The linear interval equations were changed into two standard linear programming problems, and the mathematical proof was given. By the interface program with the finite element analysis(FEA) software ANSYS and the interval computation program, the method was extended to the practical engineering area. The static response intervals were estimated by taken example for a long-span steel framing building. The results show that this method can not only give the result as exact as the traditional Deif-s method, but also have the less calculation times. The interface program with the FEA software ANSYS and the interval computational program can be used for solving the problems of practical engineering structures, directly.
Qiu Z P. Comparison of static response of structures using convex models and interval analysis method[J].International Journal for Numerical Methods in Engineering.2003,56:1735-1753
Qiu Z P, Ma Y, Wang X J. Comparison between non-probabilistic interval analysis method and probabilistic approach in static response problem of structures with uncertain-but-bounded parameters[J].Communications in Numerical Methods in Engineering.2004, 20(4):279-290
McWilliams S. Anti-optimization of uncertain structures using interval analysis[J].Computers & Structures.2001, 79(4):421-430
Deif A. Advanced matrix theory for scientists and engineers[M]. England:Abacus Press,1991
Koyluoglu H U, Cakmak A S, Nielsen A R K. Interval algebra to deal with pattern loading and structural uncertainties[J].Journal of Engineering Mechanics.1995, 121(11):1149-1157
Qiu Z P, Wang X J, Chen J Y, Exact bounds for the static response set of structures with uncertain-but-bounded parameters[J].[J].International Journal of Solids and Structures.2006,43:6574-
Dong W, Shah H C. Vertex method for computing functions of fuzzy variables[J].Fuzzy Sets and Systems.1987, 24:65-78