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

ROBOT, CYLINDRICAL COORDINATE

CYLINDRICAL COORDINATE

Re-heat nozzles in aircraft engine, Re-Heat Nozzles : If re-heat was fi...

Re-Heat Nozzles : If re-heat was fitted to an engine with a standard sized fixed area propelling nozzle, the expansion of gases caused by the use of re-heat would increase the

Counter, Design a recycling MOD 19 up counter using JK FFs. In your design,...

Design a recycling MOD 19 up counter using JK FFs. In your design, include the logic circuit diagram and the timing diagram output that counts from 000002 = 010 to 100112 = 1910. C

Design project, im on my final year, My final project is to design a 2 stor...

im on my final year, My final project is to design a 2 story office building, i was wondering if i can get any help from this website

Problem, the royal canadian hillies plan to locate a brandy carryout in the...

the royal canadian hillies plan to locate a brandy carryout in the Yukan.A number of saint Bernard dogs ,trained by sergeant preston ,will be used to rescue lost tourists looking f

Cash Flows Components, A typical investment will have three components of c...

A typical investment will have three components of cash flows: • Initial investment • Annual net cash flows • Terminal cash flows. Initial investment Initial investme

Beam theory method , Here, it is assumed that the crack is effectively long...

Here, it is assumed that the crack is effectively longer than the value measured on the side of the specimen. If one assumes that it is longer by an amount Δ, then the new crack le

Composite materials - notation of axes, Notation for Body Axes The stan...

Notation for Body Axes The standard notation for the body axis sytem for aircraft dynamics. This sectionexplains the signi?cance of the term body axis and develops the non-line

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