The finite element method fem, engineering, Other Engineering

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.
Posted Date: 2/5/2012 1:37:51 PM | Location : United States







Related Discussions:- The finite element method fem, engineering, Assignment Help, Ask Question on The finite element method fem, engineering, Get Answer, Expert's Help, The finite element method fem, engineering Discussions

Write discussion on The finite element method fem, engineering
Your posts are moderated
Related Questions
dc load line for a diode & same for circuit consisting of supply voltage in series with resistance & diodes

Net working capital In computing net cash flows in the above example, we have assumed that all revenues are received in cash and all expenses are paid in cash. In reality, the act

analysis of dual input unbalanced output differential amplifier ac analysis?

characteristic equation The characteristic equation (C.E.) corresponding to the linear state space equations comprising the state equation? x = Ax + Bu and output equatio

Engineering Signals A signal is a variation of a measurable quantity that conveys information about the behaviour of a system. • A signal can depend upon a single variable o

Your company is considering a machine that will cost $6,287 at Time 0 and which can be sold after 3 years for $790. To operate the machine, $886 must be invested at Time 0 in inven


two frames are not joint properly so create gap between two frames so material lick from this gap

how to write code for any particle shape using KK-3 system coding in grope technology

How to draw diagrams for Rankine cycle