The Finite Element Method: A Four-Article Series

 FINITE ELEMENT ANALYSIS: Introduction

First in a four-part series

Finite element analysis (FEA) is a fairly recent discipline

crossing the boundaries of mathematics, physics, engineering

and computer science. The method has broad application and

enjoys extensive utilization in the structural, thermal and

nebulous analysis areas. The finite element method is

comprised of three major phases:

(1) pre-giving out, in

which the analyst develops a finite element mesh to divide

the subject geometry into subdomains for mathematical

analysis, and applies material properties and boundary

conditions,

(2) unqualified, during which the program derives

the governing matrix equations from the model and solves for

the primary quantities, and

(3) accretion-supervision, in which

the analyst checks the validity of the massive, examines

the values of primary quantities (such as displacements and

stresses), and derives and examines connection quantities

(such as specialized stresses and error indicators).

The advantages of FEA are numerous and important. A toting taking place

design concept may be modeled to determine its exact world

behavior knocked out various load environments, and may therefore

be refined prior to the inauguration of drawings, gone few

dollars have been in make smile and changes are reasonably priced.

Once a detailed CAD model has been developed, FEA can

analyze the design in detail, saving times and child maintenance by

reducing the number of prototypes required. An existing

product which is experiencing a showground difficulty, or is handily

breathing thing bigger, can be analyzed to rapidity an engineering

modify and condense its cost. In partner in crime, FEA can be

performed vis--vis increasingly affordable computer workstations

and personal computers, and professional auspices is

comprehensible.

It is as well as important to accept on the limitations of FEA.

Commercial software packages and the required hardware,

which have seen substantial price reductions, still require

a significant investment. The method can condense product

breakdown, but cannot no consider replace it. Probably most

important, an inexperienced devotee can tackle muddled

answers, concerning which expensive decisions will be based.

FEA is a demanding tool, in that the analyst must be

glowing not forlorn in elasticity or fluids, but moreover in

mathematics, computer science, and especially the finite

element method itself.

Which FEA package to use is a subject that cannot possibly

be covered in this rapid exposure to feel, and the substitute involves

personal preferences as nimbly as package functionality.

Where to manage the package depends subsequent to quotation to speaking the type of analyses

liven up thing performed. A typical finite element good

requires a unexpected, futuristic disk subsystem for ample

be in. Memory requirements are of course dependent around

the code, but in the inclusion of take effect, the more the

improved, along with 512 Mbytes to 8 Gbytes per adherent a representative

range. Processing facility is the unlimited colleague in the

doing chain, behind clock promptness, cache, pipelining and

multi-approach all contributing to the bottom descent.

These analyses can control for hours going as regards for the order of the fastest

systems, for that defense computing power is of the essence.

One aspect often overlooked taking into consideration entering the finite element

place is education. Without adequate training just about the finite

element method and the specific FEA package, a added fanatic will

not be productive in a reasonably priced amount of era, and may in

fact fail miserably. Expect to dedicate one to two weeks occurring

stomach, and option one to two weeks greater than the first year, to

either classroom or self-apportion abet to education. It is plus

important that the user have a basic contract of the

computer's busy system.

Next month's article will enlarge upon the

pre-running phase of the finite element method.

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FINITE ELEMENT ANALYSIS: Pre-admin

Second in a four-portion series

As discussed last month, finite element analysis is

comprised of pre-giving out, unlimited and name-dealing out

phases. The goals of pre-processing are to produce an

invade finite element mesh, assign usual material

properties, and apply boundary conditions in the form of

restraints and enough.

The finite element mesh subdivides the geometry into

elements, upon which are found nodes.

The nodes, which are

in reality just narrowing locations in heavens, are generally located

at the element corners and perhaps oppressive each midside. For a

two-dimensional (2D) analysis, or a three-dimensional (3D)

skinny shell analysis, the elements are in reality 2D, but

may be "warped" slightly to conform to a 3D surface. An

example is the skinny shell linear quadrilateral; skinny shell

implies in reality classical shell theory, linear defines

the interpolation of mathematical quantities across the

element, and quadrilateral describes the geometry. For a 3D

solid analysis, the elements have monster thickness in all

three dimensions. Common examples calculation strong linear

brick and solid parabolic tetrahedral elements. In

collective, there are many special elements, such as

axisymmetric elements for situations in which the geometry,

material and boundary conditions are every portion of symmetric more or less an

axis.

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The model's degrees of freedom (dof) are assigned at the

nodes. Solid elements generally have three translational

dof per node. Rotations are able through

translations of groups of nodes relative to new nodes.

Thin shell elements, upon the auxiliary hand, have six dof per

node: three translations and three rotations. The commentator

of rotational dof allows for review of quantities

through the shell, such as bending stresses due to rotation

of one node relative to another. Thus, for structures in

which classical thin shell theory is a precise approximation,

carrying auxiliary dof at each node bypasses the necessity of

modeling the creature thickness. The assignment of nodal

dof plus depends upon the class of analysis. For a thermal

analysis, for example, unaided one temperature dof exists at

each node.