Transcript Slide 1

Available elements in SWS when discretising a model
A Lozzi 2013
shown below is a pipe elbow represented with a variety of elements.
The simplest are beam elements
that can be used to represent
welded or a pin-jointed frames.
They begin straight, but take
cubic outlines under load. They
may have up to 6 DoF at their
ends.
Shell elements shown above, are
the simplest 2 & 3D elements.
They have no thickness. These
are the earliest elements, with lots of
problems but also lots of specialised
adaptations. They may be straight or with
second order curved sides and stress
distribution.
Next SWS makes available H elements
(above). These are tetrahedrons with
straight or second order sides and stress
distribution
Finally, SWS provides P elements with
sides that are defined by polynomials,
from the 2nd to 5th order, in shape and
stress distribution. The number of nodes
per element can be increased, from 4 to
10, these are used to check if an
element becomes excessively distorted,
when fitted to a highly curved surface.
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Defaults element
size, usually very
effective
H elements.
P elements
with curved edges
Allowed variation in
element size.
Number of element
around a circle.
Variation in size of
adjacent elements.
Allows the mesher to
search for largest
element size that will
mesh fully
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H elements vary in size, P elements can vary in size and polynomial order
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Note that the deformation plot, at left,
show changes in all edge shapes, except
for the restrained left face. This
produces errors at that end of the plate.
We could have defined equal and
opposite forces on left and right faces,
then using ‘soft springs’ to balance the
numerical errors in the final calculations.
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It is possible to sections through
the Stress plot.
Von Mises and principal stresses
are available, showing pure
tension at the surface at right,
compression pressure between
surfaces in contact.
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Default mesh shown above. Note there is 2
elements through the thickness of the plate
Top left shows an example of probing, Large element size
limit the ability to pick the highest stress location. But, the
table shows that 7 fold increase in number of elements
does not have a huge effect in this case on the calculated
highest stress.
For most components the default mesh size is very effective
and you do not have to grow old waiting for an answer.
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The available options on colour range and numerical precision are shown.
Note that from the previous example , it is obvious that to quote stress to
more than 2 significant figures is just misleading.
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A model with a perfectly sharp corner, in principle
produces infinitely high stress at that corner. Hence
higher and higher mesh density results in higher and
higher maximum stress, as is shown on table below.
If a malleable material like low carbon steels were used,
then yielding at the corner would result in formation of a
fillet. A brittle material would develop a crack from the
corner.
SW advises that uncertainty of the
‘true’ stresses are caused least by
modelling, most by unrealistic
fixtures.
Uncertainty (errors) in material
properties is at least in the order of
5% from reputable suppliers, which
is further degraded by surface and
internal defects, during
manufacture. Consider then the
total uncertainty in the actual
stresses in a particular component.
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All contacts between parts in an assembly (ie top level) are by
default presumed to be bonded.
Each pair of contacting surfaces may be changed to ‘no
penetration’ or other, by progressively selecting and
redefining them.
Contacting faces may be automatically detected by using:
Tools/Interference detection/Options - select treat
coincidence as interference – calculate.
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Selection of solver methods
Direct Sparse arrives at exact
solutions . Good for models of
100,000 DoF or less. FFFPlus is
an iterative method, better for
larger models and multiple
contacts. Automatic, allows
the system to chose the solver.
Soft Spring - surrounds the
model with relatively very
soft restraints. Inertial
Relief – adds equal and
opposite forces to any small
unbalanced resultant.
Adaptive methods allows
the system to iterate to
reach acceptable errors.
Very slow and requires
experience to apply
reasonably
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SW in one of their training courses, uses the bracket
shown at left as an example of their Adaptive mesh
capability.
Presumably they put this forward as an exemplary
application of the use of Adaptive mesh generation,
but I think it could be improved upon.
At top is the model of finished part.
Below it is the simplified model which is meshed.
Note – the chamfers on all outer edges are removed
because convex corners do not increase stress. Their
removal will make the model simpler and quicker.
The fillet at the T junction must be kept because this
will generate stress concentration.
The back surface has been reshaped by flattening it.
The fillets on the rear face would caused higher than
average stresses, but they are now removed.
Also the stress at the front fillets will now be enhanced
because they now are closer to a fixed face, than they
had originally been.
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The P adaptive mesh generation, left the mesh size and distribution as originally developed.
This method increased the variation of edge and stress distribution within the elements to
the maximum 5th order polynomial.
The H method refined the mesh in areas of high stress, to about 1/10th their original size.
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What are the true stresses ?
Possibly the most accurate estimation was
obtained by photo elastic studies using near clear
plastics and polarised light. Many of these studies
support the stress concentration factors seen at
the back of many references. Typically today’s FEA
do not produce the resolution comparable with
those of past polarised light studies.
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