The finite element method fem, engineering, Other Engineering

The finite element method
The finite element method (FEM), sometimes referred to as finite element analysis (FEA), is a computational technique used to obtain approximate solutions of boundary value problems in engineering. The finite element method owes its origins to three different fields-Mathematics, Physics, and Engineering. The method was originally developed to study thestresses in complex air-frame structures (Clough 1960) and was later extended to the general field of continuum mechanics (Zienkiewicz and Cheung 1965). There have been many articles on the history of finite elements written by numerous authors with conflicting opinions on the origins of the technique (Gupta and Meek 1996; Oden 1996; Zienkiewicz 1996). The finite element method is receiving considerable attention in engineering education and in industry because of its diversity and flexibility as an analysis tool.. Greenstadt (1959) outlined a discretization approach involving “cells” instead of points. This approach contained many of the essential and fundamental ideas that serve as the mathematical basis for the finite element method. Research has shown that this method is appropriate and of negligible error in solving problems associated with engineering systems.
The finite element method considers a complicated domain to be subdivided into a series of smaller regions in which the differential equations are approximately solved. By assembling the set of equations for each region, the behaviour over the entire problem domain is determined. Each region is referred to as an element and the process of subdividing a domain into a finite number of elements is referred to as discretization. Elements are connected at specific points called nodes and the assembly process requires that the solution be continuous along common boundaries of adjacent elements.
Simple stated by Huebner and Thornton (1982), the finite element analysis can be obtained by:
Discretizing the continuum: by replacing it by a series of simple, interconnected elements where the field properties will be relatively easy to compute.
Select the interpolation function: that shows the variation of the field variable across the element domain.
Find the element properties: by substituting discrete values for the field variable at the nodes. This leads us to a system of equations.
Assemble the nodes: by combining each element approximation of the field variable to form a piecewise approximation of the behaviour over the entire solution domain.
Apply the boundary conditions that indicate the uniqueness of the solution.
Solve the system of equations using numerical techniques at each node.
Make additional computations, visualization and optional analysis using computer software.
Posted Date: 2/5/2012 1:37:51 PM | Location : United States







Related Discussions:- The finite element method fem, engineering, Assignment Help, Ask Question on The finite element method fem, engineering, Get Answer, Expert's Help, The finite element method fem, engineering Discussions

Write discussion on The finite element method fem, engineering
Your posts are moderated
Related Questions
simplify using k-map f=sum(0,4,5,6,9,10,12)+d(1,15)

Wave function is a complex quantity, which itself has no physical significance. But square of its magnitude gives the probability of finding a particle in a given volume of space a

Vibration Analysis Gas turbine engines have extremely low levels of vibration compared to piston engines. Changes in vibration levels could occur therefore without being notic

Calculate the maximum range when radar operates at 10GHz and has peak power=10 Mwatt,S/N ratio=10dB,antenna cross section=100 mm2,target cross section=10mm2.The gain of transmittin

Direct probe,isolation probe,high impedence probe,active probe,current probe

critically analyses the system design process of a project for a light railway link for a city

Rajender Kumar was a production worker at competent Motors Limited (CML) which made components and accessories for the automotive industry. He had worked at CML for almost seven ye

Framework In the laboratory we will deal with low speed flows, at first using the potential flow solver. We will also investigate behaviour for the NACA 4-series of aerofoils.


Hollow cylinders are useful building structures commonly used for both industrial and domestic purposes. Tanks, cars and some transport machineries are all applications of inner-in