Non-probabilistic uncertain static responses of imprecisely defined structures with fuzzy parameters

Abstract

In this paper fuzzy finite element method has been used for non-probabilistic static analysis of imprecisely defined structures. Uncertainties are assumed to be present in the external load, material and geometric properties of the structures, which are modelled here through the triangular convex normalized fuzzy sets. In general fuzzy finite element method for static analysis of structures converts the problem into a Fully Fuzzy System of Linear Equations (FFSLE). As such a new method has been proposed based on a linear programming problem approach to solve FFSLE. In this approach first the sign of the solution vector is determined and then accordingly interval based fuzzy arithmetic is used with linear programming to have the final solution. Practical problems viz. six bar truss and rectangular sheet have been taken into consideration for the present analysis. Also the obtained results are compared with the existing results in special cases to illustrate the efficiency and reliability of the proposed method.