Fuzzy optimization of cantilever beam

Abstract

It happens very often that we want to design a cantilever beam, while all project requirements are not fully known. Namely, we know roughly what the structure should realize. In classical optimization standard procedure should be applied in order to satisfy all the pre-requirements. What happens if the requirements can only be described, but not explicitly set? This paper starts from the premise that some requirements are expressed linguistically. We want that the length and the largest deflection of a cantilever beam are suitable to satisfy the predetermined conditions. Also, the goals are that the bending stress and the largest deflection have to be less than the allowable maximum value. The objective of this paper is: on known constraints and known fuzzy goal functions we must execute fuzzy projecting of a beam. Constraints are: the length of cantilever beam and its deflection, while the goal functions are maximum bending stress and maximum deflection. On this basis, with known cross-sectional dimensions, we can determine the maximum cantilever beam load.