The finite element method fem, engineering, Other Engineering

Assignment Help:
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.

Related Discussions:- The finite element method fem, engineering

Matlab, Provided a 1D array of integers, find all combinations of 3 values ...

Provided a 1D array of integers, find all combinations of 3 values from this set such that: a+b+c=0 For example, if one were provided with the set [3 1 3 -4 -6], the resulting answ

Skeleton pattern, A half skeleton pattern for a hollow pipe is shown. Since...

A half skeleton pattern for a hollow pipe is shown. Since the pipe is symmetrical about the pouring line, the same pattern will serve the purpose of moulding both the halves in two

Photoelectric effect, When light of frequency greater than threshold freque...

When light of frequency greater than threshold frequency fall on a metal surface, electrons are emitted out from metal surface this effect is known as photoelectric effect. Laws

Gas Furnace, Furnace limit switches are wired in series with the?

Furnace limit switches are wired in series with the?

Actuators , Actuators  The actuator consists of the control surfaces...

Actuators  The actuator consists of the control surfaces and associated servomechanisms, and is used to change the missile attitude and trajectory or flight path.

Schottky diode, working,V-I characteristics,applications and construction o...

working,V-I characteristics,applications and construction of schottky diode?

Naval architecture and marine engineering, i have a coursework for finite e...

i have a coursework for finite element analysis of marine structure and i need help to solve it

Engineering economy , A project has a first cost of $2000. There is another...

A project has a first cost of $2000. There is another cost at the end of year 1 of $500 and the income for year 3 until 6 year is $1000 per year. If the compounding is quarterly, c

Armature cipl, in which type of armature winding Equaliser ring dummy coils...

in which type of armature winding Equaliser ring dummy coils are used

Heat exchanger designing, How to design heat exchanger project from aromati...

How to design heat exchanger project from aromatics from shale gas transport phenomena, CHE 306

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd