Meshing techniques

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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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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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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Meshing techniques