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

Finite Element Analysis Assignment, Need help using FEA/FEM software (MSC M...

Need help using FEA/FEM software (MSC Marc/Mentat) to model and analyze a system,then write a lab report about it, it is due tomorrow... anything you can do for me?

Aeroengine - velocity trinagle, If radial velocity is neglected, for a stat...

If radial velocity is neglected, for a stat or there is no change from the cascade analysis. For a rotor this vectorial For a rotor this vectorial addition gives rise to graphical

Engine fuel control systems - aircraft engine, Engine fuel control systems:...

Engine fuel control systems: The thrust of a turbo jet is controlled by varying the amount of fuel that is burnt in the combustion system and in order to operate the safe tempe

Corporate Strategy, Corporate Strategy Strategy In our earlier discussion...

Corporate Strategy Strategy In our earlier discussion, we made distinctions between merger and acquisition or takeover. However, they generally involve similar analyses and evalu

Function generator, Expertsmind.com brings you unique solution in electri...

Expertsmind.com brings you unique solution in electrical engineering   What is a function generator? A function generator is a part of electronic device that prod

Corporate finance., The firm is considering an investment opportunity. The ...

The firm is considering an investment opportunity. The investment falls in the same class of risk as the firm, the project is financed with equity and debt. Explain all the steps i

Homework, 1) An investment project requires a net investment of $100,000. T...

1) An investment project requires a net investment of $100,000. The project is expected to generate annual net cash flows of $28,000 for the next 5 years. The firm''''s cost of cap

Thermo electric thermometer, how thermoelecteric thermometer is contructed ...

how thermoelecteric thermometer is contructed and how it working

Traffic management, (a) Discuss the requirements, specifications and specia...

(a) Discuss the requirements, specifications and special requirements for the  design of arterial road networks and residential area street networks in a developing suburban region

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