A Convex Combination-Based Approach for Uncertain Static Responses of Structures Subjected to Fuzzy External Loadings

In this paper, the uncertain static responses of structures under fuzzy external loadings are investigated using the fuzzy finite element approach. External loads are represented as fuzzy values in this study, although material and geometric properties are regarded as precise. Accordingly, the obtained governing static equilibrium equations is a fuzzy system of linear equations with crisp coefficients, fuzzy unknowns, and a fuzzy right-hand side vector. To solve this fuzzy system, a novel method based on the concept of convex combinations is proposed. The method leverages convex combinations after converting the fuzzy system into an analogous interval form in order to produce a crisp system representation. To obtain the ultimate solution, the resulting crisp systems are solved for two distinct parametric values of the convex combination together. The work examines a mathematical example in addition to actual examples such as an 8-bar truss, a fixed-fixed beam, and a uniform rectangular sheet subjected to external loads. The results are validated by comparing the obtained results with existing techniques.