Fuzzy optimum design of aseismic structures

AbstractIt was pointed out in our previous paper that there exists a vast amount of fuzzy information in both objective and constraint functions of optimum design of structures. Then the idea of fuzzy optimum design of structures was first proposed and the problem with fuzzy allowable intervals of the physical variables (structural responses and sizes) could be solved via the α‐level cut approach.In this paper, the procedure of fuzzy optimum design of aseismic structures is further developed. For this purpose, the concepts and definitions of fuzzy predictive earthquake intensity, fuzzy response spectrum and fuzzy structural response are given. A solution of the programming problems with generalized fuzzy constraints (including both fuzzy constraint functions and their fuzzy allowable intervals) is put forward; one of its special cases is the χ‐level cut solution in Reference 1. The satisfaction degree of a fuzzy constraint function to its fuzzy allowable interval is defined, by which the problem considered is transformed into a series of non‐fuzzy programmings. Then, a series of optimum points can be obtained which make up the solution of the fuzzy programming.As the solution of fuzzy programming contains not one but a series of optimum points, a two‐step approach is presented to the fuzzy optimum design of aseismic structures. The first step is to find out the set of minimum cost design points corresponding to different design levels. In the second step, both construction cost and earthquake‐caused loss expectation in the service life of the structure are traded off to find the optimum design level as well as a corresponding optimum design scheme.