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

Aviation legislation design and type certificate, Design, Construction and ...

Design, Construction and Type Certificate The following chapter covers the initial design, construction, registration and test flying of the first prototype of a new aircraft.

Fire evacuation - railway inspections, Fire evacuation - Railway inspection...

Fire evacuation - Railway inspections: Fire evacuation signals should be given by voice messages and these must be easily understood by the occupants. The expected populati

Integrated circuits, Integrated circuits: Integrated circuits, or IC's,...

Integrated circuits: Integrated circuits, or IC's, have changed the entire electronics industry. Before IC's were developed, all electronic circuits consisted of individual (d

Heat treatment., Why low carbon steel can not be quench hardened?

Why low carbon steel can not be quench hardened?

Propeller spinners, PROPELLER SPINNERS All modern propeller-driven aero...

PROPELLER SPINNERS All modern propeller-driven aeroplanes have spinners over their propeller hubs. These spinners have the dual aerodynamic function of streamlining the engine

sweep effects, In the previous discussion, we investigated the static aero...

In the previous discussion, we investigated the static aeroelastic behaviour of straight (unswept) wings. These wings are characterised by an effective decoupling of wing bending a

Numerical methods, Numerical solutions to equations: Many practical p...

Numerical solutions to equations: Many practical problems in engineering involve complex boundary conditions and variable properties that cannot be solved analytically, creat

Water, Dear Sir, Please answer the follwing question . Specs: Filterati...

Dear Sir, Please answer the follwing question . Specs: Filteration Capacity 18000 LPH , Tested pressure 6Kg/Sq.cm, Vertical MS pressure Sand filter(flat ends 6mm thick & di

Bme, advantages and disadvantages oh hot and cold die working in the subjec...

advantages and disadvantages oh hot and cold die working in the subject of basic mechanical engineering

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