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

Programming of 18F4550, #include org 0xoo movlw 0x00 ---------- movlw 0xff ...

#include org 0xoo movlw 0x00 ---------- movlw 0xff movwf PORTB end

Crystal structure, how can we determine the crystal structure of material b...

how can we determine the crystal structure of material by having interplanar spacing d?

Mine Surveying.., Question 1 (100 marks) As Surveyor in charge of an underg...

Question 1 (100 marks) As Surveyor in charge of an underground mine you have been instructed to design a tunnel to join a crosscut to a haulage drive. The details of the crosscut a

Prepare a short document to sensitise public, Since the introduction of mob...

Since the introduction of mobile phones and other smart devices, concerns (both scientific and public) have been raised about the potential health impacts from regular use. Numerou

Boroscope inspections of air craft engine, Boroscope inspections: Boros...

Boroscope inspections: Boroscope inspections involve looking at components within an engine using an optical probe. The probes are inserted in to the engine through ports in th

Mba financial management , Which type of financing is appropriate to each f...

Which type of financing is appropriate to each firm caselet

Oscilloscope probes, Direct probe,isolation probe,high impedence probe,acti...

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

Choked nozzle and thrust correction - turbojet, Choked Nozzle Consideri...

Choked Nozzle Considering the formula for thrust under "choked" nozzle conditions: Thrust =(P-P 0 )A + WV j /g     Where: P = Pressure P = Ambien

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