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Introduction
to Finite Element Analysis
Finite Element Analysis is a computerized
method for predicting how a component/assembly
will react to environmental factors such
as forces, heat and vibration. It is called
"analysis", but in the product
design cycle it is used as a "virtual
prototyping" tool to predict what is going
to happen when the product is used.
Finite element analysis, as related to
the mechanics of solids, is the solution
of a finite set of algebraic matrix equations
that approximate the relationships between
load and deflection for static analysis
as well as velocity, acceleration and
time for dynamic analysis.
In 1678, Robert Hooke set down the basis
for modern finite element stress analysis
as Hooke's Law. Simply, an elastic body
stretches (strain) in proportion to the
force (stress) on it.
Mathematically:
F=kx.
- F = force
- k = proportional constant
- x = distance of stretching
This is the only equation you need to
know to understand linear finite element
stress analysis.
The finite element method works by breaking
a real object down into a large number
(1000's or 100,000's) of elements (e.g.
cubes). The behavior of each little element,
which is regular in shape, is readily
predicted by set mathematical equations.
The summation of the individual element
behaviors produces the expected behavior
of the actual object.
The "finite element"
is a small, but not infinitesimal, part
of the mechanical structure being modeled
that incorporates complex strength of
materials formulations into a relatively
simple geometric shape. The simplest examples
are rods, beams and triangular plates.
More complicated elements include quadrilateral
plates, curved shells and 3-dimensional
solids such as hexahedrons (bricks).
The "Finite" in Finite Element
Analysis comes from the idea that there
are a finite number of elements in a finite
element model. Previously, engineers employed
integral and differential calculus techniques
to solve engineering analysis problems.
These techniques break objects down into
an infinite number of elements, for problem
solving.
Finite
Element Analysis Process
Finite Element Modeling
Finite Element Analysis begins with the
finite-element modeler (sometimes called
a mesher or preprocessor). The cost-effectiveness
of FEA is heavily dependent on the Pre-Processor
since the vast majority of human time
involved in Finite Element Analysis is
spent in creating the model for analysis.
In order to effectively incorporate analysis
into the design cycle, you must be able
to quickly create the required models.
The modeler creates the physical data
necessary for analyis by creating a mesh
of elements utilizing either an imported
3D CAD model or one generated internally.
There are two basic mesh types characterized
by the connectivity of their points. Structured
meshes have a regular connectivity, which
means that each point has the same number
of neighbors (for some grids a small number
of points will have a different number
of neighbors). Unstructured meshes have
irregular connectivity (e.g. each point
can have a different number of neighbors.)
Unstructured meshes have been developed
mainly for the finite element method.
There is a large range of possible shapes
for finite elements: tetrahedra, prisms,
blocks, and there can be arbitrary connectivity,
leading to unstructured meshes. Meshes
can be generated fully automatically using
triangles in 2D and tetrahedra and now
blocks in 3D.
Finite Element Solvers
Solvers are the engines of finite-element
analysis. They take the elements, boundary
conditions, and loads and output a solution
containing all of the information needed
to review and understand results. Solvers
may be divided into two categories: linear
and nonlinear.
Linear FEA is differentiated
from nonlinear in that all deflections
are assumed small, no boundary conditions
change during the analysis and material
properties are linear (i.e., elastic).
Post Processing
Postprocessors--or visualizers--utilize
the data generated by the solver to create
easily understandable graphics and reports.
The Finite Element Method is employed
to predict the behavior of things with
respect to virtually all physical phenomena:
- Mechanical stress (stress analysis)
- Mechanical vibration
- Heat transfer - conduction, convection,
radiation
- Fluid Flow - both liquid and gaseous
fluids
- Various electrical and magnetic phenomena
- Acoustics
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