Comparison of fuzzy set and convex model theories in structural design

A methodology for the treatment of uncertainty in the loads applied to a structural system using convex models is presented and is compared to the fuzzy set finite-element method. The analytical results for a beam, a truss and a frame structure indicate that the two methods based on convex model or fuzzy set theory are in good agreement for equivalent levels of uncertainty applied to linear structures. Convex model or fuzzy set theories have shown that the worst-case scenario response of all possible load combinations cannot be captured simply by load factorisation, as is the current design practice in building codes. Design problems including uncertainty with a large number of degrees of freedom, that are not computationally feasible using conventional methods described in building codes, can be solved easily using convex model or fuzzy set theory. These results can be used directly and efficiently in the analyses required for the optimal design of structural systems, thus enabling optimisation of complex structural systems with uncertainty.