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

Swell Factors, The effect of swell factors on volumes

The effect of swell factors on volumes

How does plane diffraction grating forms a spectrum?, Q.  With necessary t...

Q.  With necessary theory explain the formation of spectrum by a plane transmission grating when composite light falls on it OR How does plane diffraction grating for

Pov display, require help in making pov display

require help in making pov display

Feathering the propeller, Feathering the propeller: If there is an engi...

Feathering the propeller: If there is an engine failure in flight, the propeller would windmill creating drag and increasing any damage that had occurred in the engine. Feathe

Themodynamic, 1 kg of air is allowed to expand reversibly in a cylinder beh...

1 kg of air is allowed to expand reversibly in a cylinder behind a piston in such a way that the temperature remains constant at 260 degree while the volume is doubled.The piston i

Measurement of thermocouple voltage, Measurement of thermocouple voltage ...

Measurement of thermocouple voltage The voltage is typically only a few millivolts and should be measured using a high impedance system. If an amplifier is used, must also have

FI560, Each student will, as part of the course requirements, submit a rese...

Each student will, as part of the course requirements, submit a research paper on an individual stock. You are allowed to select any stock that trades on the New York Stock Exchang

Logic gate -xor gate, 'Exclusive or' gate: The basic OR gate illustrate...

'Exclusive or' gate: The basic OR gate illustrated previously in Figure 3 was seen to include the AND operation in that its output will adopt the 1 state not only when either i

Ts diagram, how to find points on Ts diagram?

how to find points on Ts diagram?

Circuit analysis, One thing I have always thought that experienced repair p...

One thing I have always thought that experienced repair people knew about was circuit analysis. I always imagined that when looking at schematics I would be able to figure the vol

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