## Description

Write an essay (some text about a given topic) of 1200 words with text only (no images, no tables, no equations, no references, no cover page) about the following term:

FEA (Finite Element Analysis)

The allowed similarity is 10%

## Explanation & Answer

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Finite Element Analysis

Finite element analysis is basically a numerical technique to solve real life problems related to

engineering and physics based mathematical modelling. The method is generally used at places

where analytical solutions that is by using generalized equations cannot be obtained, for

example problems with complicated geometries, loadings and material properties.

To clarify it we can take example of truss, beam etc. whose stress analysis has to be done. This

can be done by using design equations based on loading conditions and equilibrium equations.

Hence, this is analytical method which is used for the normal problems where accuracy

requirement is less and are generally used as for preliminary estimation of a quantity but when

it comes to the complex problems and accuracy requirements are higher, finite element method

is used. For example, when we need to understand the physical behaviors of complex objects

such as heat transfer through a body, fluid flow through section of a river or pipe. This method

is also used to check the accuracy and performance of design such as safety margin and

identifying the weakness in design. Various conditions are tested to get the optimum design.

Finite element method is a method of solving partial differential equations in two or three space

variables which is closed in nature or the boundary value problem. Here, boundary values are

the specified values of field variables on the boundary of the field which are the dependent

variables of interest governed by the differential equations. To solve a problem, this method

uses the first step known as discretization in which this method divides large system into

smaller systems which are called finite elements. Discretization is a process in which the mesh

is constructed around the object in the area of interest which is also called numerical domain

of the object and is done in the space having finite number of points. This process leads to the

formation of boundary value problem which finally results in the formation of system of

algebraic equations. The method further calculates the unknown function over the domain. This

simple equation used for the domain is further used for the larger system of equations to solve

the entire problem. The FEM further uses calculus of variations in which variations, which are

small changes in functions which is used to maximize or minimize the functions is used to

approximate a solution by minimizing the error function.

Finite element method is not so old method and was first implemented in the early 1940s by

the scientists A. Hrennikoff and R. Courant to solve elasticity and structural analysis problems

those were complex in nature. K Feng named Chinese scientist proposed a systematic

numerical method in 1950s and 1960s for solving partial differential equations for the purpose

of computations for dam construction and the method was called finite difference method based

on variational principle. The approaches of all the scientists were different but one essential

characteristic wa...