Finite Element Method

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 equ...

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Bibliographic Details
Published in:Advanced Numerical and Semi-Analytical Methods for Differential Equations pp. 63 - 80
Main Authors: Chakraverty, Snehashish, Mahato, Nisha, Karunakar, Perumandla, Dilleswar Rao, Tharasi
Format: Book Chapter
Language:English
Published: United States Wiley 2019
John Wiley & Sons, Incorporated
John Wiley & Sons, Inc
Edition:1
Subjects:
algebraic equations
dynamic analysis
eigenvalue problems
finite element method
Galerkin method
linear second‐order ordinary differential equation
partial differential equations
static conditions
structural mechanics
Interpolation
Three-dimensional displays
Shape
Two dimensional displays
Boundary conditions
Finite element analysis
Method of moments
ISBN:9781119423423, 1119423422
Online Access:Get full text
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Summary: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.
ISBN:9781119423423
1119423422
DOI:10.1002/9781119423461.ch6