Interval Finite Element Method - Chakraverty, Snehashish; Mahato, Nisha; Karunakar, Perumandla; Dilleswar Rao, Tharasi (Advanced Numerical and Semi-Analytical Methods for Differential Equations, 2019)
Finite element method (FEM) combined with interval uncertainties are referred to as interval FEM which has already been used in various structural systems. On the other hand, for fuzzy uncertainties FEM is known as fuzzy FEM discussed for uncertain structural systems. In structural mechanics, the FEM converts the governing differential equation of static and dynamic problems of structural systems having interval uncertainties to interval system of equations and interval eigenvalue problem, respectively. In this regard, the chapter presents the introduction and preliminaries related to system of equations and eigenvalue problems with uncertain (in terms of interval) parameters. It provides a detailed procedure for solving ordinary differential equation subject to interval boundary conditions using Galerkin FEM. As such, the authors refer the Galerkin FEM for solving differential equation with interval uncertainties as uncertain IGFEM. Lastly, the chapter considers uncertain static and dynamic analysis of one‐dimensional structural system.