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) has wide applications in various science and engineering fields viz. structural mechanics, biomechanics and electromagnetic field problems, etc. of which exact solutions may not be determined. It serves as a numerical discretization approach that converts differential equations into algebraic equations. This chapter solves simple differential equations in order to have better understanding of the finite element technique. For ease of understanding the FEM, the step‐by‐step procedure of linear second‐order ordinary differential equation (ODE) is considered with respect to the Galerkin method. In structural mechanics, the approximate solution of governing partial differential equations for structures may be obtained using the FEM. Under static and dynamic conditions, the associated differential equations get transformed to simultaneous algebraic equations and eigenvalue problems, respectively. In this regard, the chapter considers static and dynamic analysis of structural systems. It also considers the FEM modeling of one‐dimensional structural system subject to static conditions.