Solving the nondeterministic static governing equations of structures subjected to various forces under fuzzy and interval uncertainty

摘要

This paper investigates the static analysis of structures subjected to uncertain loads using the fuzzy and interval finite element method. Uncertainties are considered in terms of interval and fuzzy numbers. Herein, the material and geometric properties of the structures are considered as crisp in nature. For the presented static analysis, the fuzzy and interval finite element method converts the problem into an interval and fuzzy system of linear equations. As such, the coefficient matrix and the right-hand side vector become crisp and uncertain, respectively. To solve the corresponding system, a new method based on fuzzy center and radius has been proposed using fuzzy arithmetic. Existence of solution and convexity analysis has also been investigated here. Along with these, conditions for weak and strong fuzzy solutions have been studied. Numerical examples of beam, fifteen-bar truss, and rectangular sheet with various types of uncertain loads have been considered to illustrate the computational aspects of the proposed method. (C) 2019 Elsevier Inc. All rights reserved.