Internal Gauss points

If Gauss points are to be included, they must be defined before the Result which uses them. Each Gauss points block is defined between the lines GaussPoints and End GaussPoints.

The structure is as follows, and should:

  • Begin with a header that follows this model:

GaussPoints "gauss_points_name" Elemtype my_type "mesh_name"

where

  • GaussPoints, elemtype: are not case-sensitive;
  • "gauss_points_name": is a name for the gauss points set, which will be used as reference by the results that are located on these gauss points;
  • my_type: decribes which element type these gauss points are for, i.e. Line, Triangle, Quadrilateral, Tetrahedra, Prism, Pyramid or Hexahedra ;
  • "mesh_name": is an optional field. If this field is missing, the gauss points are defined for all the elements of type my_type. If a mesh name is given, the gauss points are only defined for this mesh.

  • Be followed by the gauss points properties:

Number of Gauss Points: number_gauss_points_per_element

Nodes included

Nodes not included

Natural Coordinates: Internal

Natural Coordinates: Given

natural_coordinates_for_gauss_point_1 . . . natural_coordinates_for_gauss_point_n

where

  • Number of Gauss Points: number_gauss_points_per_element: is not case-sensitive and is followed by the number of gauss points per element that defines this set. If Natural Coordinates: is set to Internal, number_gauss_points_per_element should be one of:
  • 1, 3, 6 for Triangles;
  • 1, 4, 9 for Quadrilaterals;
  • 1, 4, 10 for Tetrahedra;
  • 1, 8, 27 for Hexahedra;
  • 1, 6 for Prisms;
  • 1, 5 for Pyramids; and
  • 1, ... n points equally spaced over lines.

For triangles and quadrilaterals the order of the gauss points with Internal natural coordinates will be this:

Internal coordinates:

( 0, 0)

Internal coordinates:

a=0.57735027

(-a,-a) ( a,-a)

( a, a) (-a, a)

Internal coordinates:

a=0.77459667

(-a,-a) ( a,-a) ( a, a)

(-a, a) ( 0,-a) ( a, 0)

( 0, a) (-a, 0) ( 0, 0)

Gauss Points positions of the quadrature of Gauss-Legendre Quadrilaterals

Internal coordinates:

a=1/3

( a, a)

Internal coordinates:

a=1/2

( a, 0) ( a, a) ( 0, a)

Internal coordinates:

a=0.09157621 b=0.81684757

c=0.44594849 d=0.10810301

( a, a) ( b, a) ( a, b)

( c, d) ( c, c) ( d, c)

Gauss Points positions of the quadrature of Gauss for Triangles

For tetrahedra the order of the Internal Gauss Points is this:

Internal coordinates:

a=(5+3*sqrt(5))/20=0.585410196624968

b=(5-sqrt(5))/20 =0.138196601125010

( b, b, b) ( a, b, b) ( b, a, b) ( b, b, a)

Internal coordinates:

a=0.108103018168070

b=0.445948490915965

c=0.816847572980459

( a, a, a) ( c, a, a) ( a, c, a) ( a, a, c)

( b, a, a) ( b, b, a) ( a, b, a)

( a, a, b) ( b, a, b) ( a, b, b)

For hexahedra the order of the Internal Gauss Points is this:

Internal coordinates:

a=0.577350269189626

(-a,-a,-a) ( a,-a,-a) ( a, a,-a) (-a, a,-a)

(-a,-a, a) ( a,-a, a) ( a, a, a) (-a, a, a)

Internal coordinates:

a = 0.774596669241483

(-a,-a,-a) ( a,-a,-a) ( a, a,-a) (-a, a,-a)

(-a,-a, a) ( a,-a, a) ( a, a, a) (-a, a, a)

( 0,-a,-a) ( a, 0,-a) ( 0, a,-a) (-a, 0,-a)

(-a,-a, 0) ( a,-a, 0) ( a, a, 0) (-a, a, 0)

( 0,-a, a) ( a, 0, a) ( 0, a, a) (-a, 0, a)

( 0, 0,-a)

( 0,-a, 0) ( a, 0, 0) ( 0, a, 0) (-a, 0, 0)

( 0, 0, a)

( 0, 0, 0)

For prisms the order of the Internal Gauss Points is this:

Internal coordinates:

a=1/6=0.166666666666666

b=4/6=0.666666666666666

c=1/2-1/(2sqrt(3)) =0.211324865405187

d=1/2+1/(2sqrt(3))=0.788675134594812

( a, a, c) ( b, a, c) ( a, b, c)

( a, a, d) ( b, a, d) ( a, b, d)

For pyramids the order of the Internal Gauss Points will be this:

Internal coordinates:

a=8.0*sqrt(2.0/15.0)/ 5.0 =0.584237394672177

b=-2/3 =-0.666666666666666

c=2/5 = 0.4

( -a, -a, b)

( a, -a, b)

( a, a, b)

( -a, a, b)

( 0.0, 0.0, c)

The given natural coordinates for Gauss Points should range:

  • between 0.0 and 1.0 for Triangles, Tetrahedra and Prisms, and
  • between -1.0 and 1.0 for Quadrilaterals, Hexahedra and Pyramids.

Note: If the natural coordinates used are the internal ones, almost all the Results visualization possibilities will have some limitations for tetrahedra and hexahedra with more than one gauss points. If the natural coordinates are given, these limitations are extended to those elements with number_gauss_points_per_element not included in the list written above.

  • Nodes Included / Nodes not Included: are not case-sensitive, and are only necessary for gauss points on Line elements which indicate whether or not the end nodes of the Line element are included in the number_gauss_points_per_element count.

The default value is nodes not included

Note: By now, Natural Coordinates for line elements cannot be "Given"

  • Natural Coordinates: Internal / Natural Coordinates: Given: are not case-sensitive, and indicate whether the natural coordinates are calculated internally by GiD, or are given in the following lines. The natural coordinates should be written for each line and gauss point.

  • End with this tail:

End GaussPoints

where End GaussPoints: is not case-sensitive.

Here is an example of results on Gauss Points:

GaussPoints "Board gauss internal" ElemType Triangle "board"

Number Of Gauss Points: 3

Natural Coordinates: internal

end gausspoints

The following Internal gauss points are automatically defined.

Results can use this names without explicitly define them with a GaussPoints / End GaussPoints statement.

GP_POINT_1

GP_LINE_1

GP_TRIANGLE_1 GP_TRIANGLE_3 GP_TRIANGLE_6

GP_QUADRILATERAL_1 GP_QUADRILATERAL_4 GP_QUADRILATERAL_9

GP_TETRAHEDRA_1 GP_TETRAHEDRA_4 GP_TETRAHEDRA_10

GP_HEXAHEDRA_1 GP_HEXAHEDRA_8 GP_HEXAHEDRA_27

GP_PRISM_1 GP_PRISM_6

GP_PIRAMID_1 GP_PIRAMID_5

GP_SPHERE_1

GP_CIRCLE_1

Is is possible to use also the generic name GP_ELEMENT_1 to mean all kind of elements with 1 gauss point (instead of the specific element GP_LINE_1, GP_TRIANGLE_1, etc.

Gauss points format

Internal Gauss points