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Finite Element Analysis (FEA) is a powerful tool that essentially divides a
complex structure up into many small elements, where for each the stresses
and deformations can be solved for using known equations of elasticity.
Because the boundaries of each element in contact with another element must
have equal and opposite forces and equal deflections, a large array of equations
can be generated and solved by computer to determine the forces and deflections
on all the elements. A critical issue is the constraints on the exterior elements
that are meant to model the connection of the part to the world. For
example, a cantilever beam has all the faces of elements at one end constrained
to not have any deflections. But what about a simply supported beam?
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FEA configures a model for analysis using a complex system of points or nodes which are connected into a grid called a mesh. This mesh has defined properties or characteristics, such as material, structural properties, elasticity, etc.. The nodes are configured with particular density throughout the model dependant on the stress levels within a particular area. Areas that are know to relize elevated stress typically have a higher node density than those areas that will see little or no stress.
There are some types of elements, plates and shells that are two
dimensional yet are assigned a thickness. These 2D elements can have an edge
constrained to be simply supported (no linear displacement) or supported so
there is no linear or angular displacement. Most design engineers creating new
designs use a solid modeling system or Computer Aided Design (CAD) software, and the solid modeler is often parametrically linked
directly to an FEA program. Herein lies the challenge, because some (not all)
FEA programs take a solid model and break it up into solid elements, where
their solid elements can only be constrained along a surface which causes a
moment constraint (no linear or angular translations) to always be imposed.
The moment constraint does not always capture the intent of the designer and
can cause a structure’s stiffness to be greatly over predicted. Fortunately, as
shown, some FEA programs do allow a solid’s edge to be displacement but not
rotation constrained. If an FEA program does not allow the edge of a solid to be simply
constrained, thin solid flexural elements can be added.
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