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8/11/2019 Meshing techniques
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Meshing
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Discretization of problem:
All real life objects are continuous. Means there is no
physical gap between any two consecutive particles. Solving
a real life problem with continuous material approach is
difficult and basic of all numerical methods is to simplify the
problem by discretizing (discontinuation). In simple words
nodes work like atoms and with gap in between filled by anentitiy called as element. Calculation are made at nodes
and results are interpolated for element.
All the numerical methods including Finite Element follows
discrete approach. Meshing is nothing but discretization of
a continuous system with infinite degree of freedoms to
finite degree of freedoms.
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What is DOF
Minimum number of parameters (motion, coordinates,
temp etc.) required to define position of any entity
completely in the space is known as degree of freedom
(dof).
Why do we carry out meshing, what is FEM
No. of points:
Dof per point: 6
Total equation :
No. of points:8
Dof per point: 6
Total equation : 48
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Aspect Ratio
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Distortion or Poor Shape of Elements:
Computed FE results tend to be most accurate when elements are
compact, without great elongation, skew, or warping
Distortion usually degraded field gradients such as stresses more than it
degrades displacements, natural frequencies, mode shapes, or
temperatures.
Elements having side nodes can better fit a curved boundary than
elements having only corner nodes.
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Abrupt changes in element size should be avoided. Even if element aspect ratio are
satisfactory in the poor arrangements, neighborhood of an abrupt element size
change.
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Changes in element type ( such as triangular to quadrilateral), abrupt
changes in element sizes, poorly shaped elements, and inappropriate
element connections all may produce artificial disturbances in the gradient
field that may mistakenly be accepted as physically realistic.
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2002 Brooks/Cole Publishing / Thomson Learning
Figure 7-1a (a) Beam with
loading: effects of the aspect
ratio (AR) illustrated by the
five cases with different
aspect ratios
Aspect ratio = longest
dimension/ shortestdimension
Aspect ratio and element shapes
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2002 Brooks/Cole Publishing / Thomson Learning
Figure 7-1b (b) Inaccuracy of solution as a function of the aspect
ratio (numbers in parentheses correspond to the cases listed in
Table 7-1)
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2002 Brooks/Cole Publishing / Thomson Learning
Figure 7-2 Elements with poor shapes
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Avoid abrupt changes in element sizes
Abrupt change in
element size
Gradual change in
element size
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Examples of how NOT to connect elements
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Natural subdivisions at discontinuities
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