Fea 1 /certified fixed orthodontic courses by Indian dental academy

FINITE ELEMENT
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INDIAN DENTAL ACADEMY
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• An engineering technique of stress analysis, the
basic concept of which is the visualization of a
structure as an assemblage of a finite number of
discrete structural elements connected at a finite
number of points. The finite elements are formed
by figuratively "cutting the original structure into
segments.

History
• 1851 – Schellbach derived a differential equation
of the surface of minimum area bounded by a
closed curve, he discretized the surface into
triangles for deriving the equation.
• 1943 – Courant determined the torsional rigidity
of a hollow shaft by discretization and using net
points ( nodes ) and deriving equations for it.

• Turner, Taig and Argyris were aeronautical
engineers who did considerable research in
this field in 1960’s.
• 1960 – Clough coined the term “FINITE
ELEMENT”.
• 1963 – FEA gained position as a proper
method for analysis.

• Late 1960 – general purpose computer programs
emerged and since then computer graphics of high
power are attached to FEA which has brought the
method to present state.
• Today about 400 computer programs are present
for FEA,as ANSYS,ADAM, PASSFEM etc.
• It was first applied to the field of orthodontics by
Moss et al in 1985 for studying cephalograms.

WHAT IS FINITE ELEMENT
METHOD
• Numerical method.
• Simulation and not reality.
• Going from part to whole approach
• Divides the structure into an equivalent
system of smaller bodies or units, the
assemblage of this units then represents the
original body.

• This smaller units are called elements and
since the number of this elements is definite
it is called finite element method.
• These elements are considered to be
connected at joints which are called nodes
or nodal points.

• For two-dimensional applications, triangles
of various sizes and shapes usually are the
finite elements of choice. Each element
retains the mechanical characteristics of the
original structure. Some characteristics of
the material have to be specified (depending
on whether it is isotropic or not).

• Additionally, a numbering system is
required to identify the elements and their
connecting points, called "nodes. " A
coordinate system also must be established
to identify uniquely the location of the
nodal points. A large number of
simultaneous linear equations are computer-
generated, which establishes compatibility
within each element.

• Analysis gets simplified considerably but
the amount of data to be handled also
increases according to the no. of smaller
units present and for a very large number of
data to be calculated a high speed computer
is needed.

• This technique has some very distinct
advantages as a research tool, among which
is the ability to obtain an estimate of the
stresses throughout the structure under
consideration. Further, the inclusion of any
type of anisotropy and inhomogeneity
conceptually is possible by inserting the
appropriate distribution of material
properties at the nodes of the elements.

• However, when it is applied to structures
such as a tooth, there are some practical
limitations, as relatively little is known
about the mechanical properties of dental
and especially periodontal tissues.

Different Approaches
• Displacement method.
• Equilibrium method.
• Mixed method.

• The change taking place at nodes can be
expressed in various simpler forms as
polynomial or trigonometric functions,
commonly used one is polynomial method.
• To obtain the set of equilibrium equations
for each element principles of mechanics as
the principle of minimum potential energy
is employed.

• Internal strain energy = ½ (force in the
spring)
(displacement)
• U = ½ Ku x u
• U = ½ Ku2
• Potential energy of external load F is
• W = (load )
( displacement from zero potential state)

• Total potential energy = ½ Ku2
– F x u
• Minimum of total potential energy can be
obtained b differentiating it with respect to
u and equating the result to 0.
• dT/du = Ku – F = 0
• Ku = F

Analysis procedure
1- discretization of structure.
2 - selection of displacement models.
3 - derivation of equilibrium equations.
4 - assembly of algebraic equations for the
whole structure.
5 - solutions for unknown displacements.
6 - computation of element stress and strain.

Solving a problem by FEA
• Classify the problem.
• Prepare a mathematical model.
• Discretize the model.
• Computers do the calculations.
• Check results.

Advantages of FEA
• An FE structure closely resembles the
actual body or region to be analyzed.
• FEA is applicable to any problem like stress
analysis, heat transfer etc.
• There is no geometric restriction, the body
or region analyzed may have any shape.
• Loading conditions are not restricted, force
applied may be distributed or concentrated.

• It is independent of method of registration or
orientation.
• Material properties are not restricted to isotropy
and may change from one element to another.
• Components that have different behaviors and
different mathematical descriptions can be
combined.
• The approximation can be easily improved by
increasing the number of elements.

Disadvantages of FEA in
orthodontics
• Landmark(nodes) location procedures are
as crude and error prone as conventional
cephalometry, as they are obtained by
radiographs only.
• The utility of FEA in the analysis of growth
and development has not been tested,
except to compare its findings with
conventional methods.It is a hypothesis
without test. www.indiandentalacademy.com

• The nodes surrounding the elements
straddle sutures and even extend from the
calvarium to mandible.this violates the
usual assumption of FEA that is within each
element the structure is homogenous.

• There is a fundamental question about applying a
mathematical model which was developed to
measure strain and deflection of structures under
mechanical loads to the process of developmental
biology in which mechanical loading is minimal
or non existent.Only forces acting in a skull are
the muscular forces which are intermittent and
irregular and gravitational, both of which are not
considered in FEA.

Thank you
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Fea 1 /certified fixed orthodontic courses by Indian dental academy

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