Fuzzy-based analysis of structures

The analysis of existing structures requires engineers to model two types of uncertainty, cognitive and non-cognitive types. The objective of this paper is to reexamine structural analysis methods by considering the cognitive type of uncertainty. Two approaches based an the displacement method for structural analysis are proposed: (1) fuzzy arithmetic approach, and (2) permutations approach. The first approach only obtains approximate solutions. The second approach produces the exact solution but requires move computing time. The behavior of fundamental structural systems was investigated and the results based on the second approach showed that if the modulus of elasticity is a triangular fuzzy number, the member forces can be either fuzzy numbers or crisp values depending on the structural system type. Modified fuzzy division and subtraction were also proposed for solving simultaneous equations with fuzzy coefficients using fuzzy arithmetic.