Brick Elements: Local Axes

Local x, y, z axes

The default local axis system of brick elements coincides with the global axis system. The axes may also be aligned to any UCS via the Brick Attributes: Local Axes attribute.

Local axes on brick elements are important for the following purposes:

Local face x, y axes (direction on brick faces)

The direction of Brick Attributes: Face Shear Stress is defined by local x, y axes on the face of a brick. These local axes match the local axes of a plate element connected directly on top of the brick face to the same nodes, with the plate element having the same shape as the brick face (i.e., triangular or quadrilateral) and connected with its normal pointing outward.

The following images illustrate the local face axes for each type of brick element.

The face definitions for each brick type (i.e., the equivalent plate corner nodes) are tabulated below.

Brick Type

Face

Equivalent Plate Nodes

Tetrahedron

1

1-2-3

 

2

4-1-3

 

3

4-2-1

 

4

4-3-2

Pyramid

1

1-2-3-4

 

2

5-1-4

 

3

5-2-1

 

4

5-3-2

 

5

5-4-3

Wedge

1

1-2-3

 

2

5-2-1-4

 

3

4-6-5

 

4

4-1-3-6

 

5

6-3-2-5

Hexahedron

1

1-2-3-4

 

2

7-3-2-6

 

3

6-5-8-7

 

4

5-1-4-8

 

5

8-4-3-7

 

6

6-2-1-5

Local u, v axes (position on brick faces)

Similar to Plate Elements: Local Axes, the position on brick faces can be described by using the local u-v coordinates. The u-v coordinate range is always defined to be between -1 and +1 for quadrilateral faces and between 0 and +1 (with some restrictions) for triangular faces.

Triangular Brick Faces

The figure below shows the u-v coordinates for triangular brick faces.

  Node Coordinates
u v
1 0 0
2 1 0
3 0 1
4 0.5 0
5 0.5 0.5
6 0 0.5

Quadrilateral Brick Faces

The figure below shows the u-v coordinates for quadrilateral brick faces.

  Node Coordinates
u v
1 -1 -1
2 1 -1
3 1 1
4 -1 1
5 0 -1
6 1 0
7 0 0
8 -1 0

Local u, v, w axes (internal position of bricks)

The position on the inside of a brick element can be described by using the local u-v-w coordinates.

The u-v coordinate range is defined to be between -1 and +1 if the base face is quadrilateral (i.e., pyramid, hexahedron), and between 0 and +1 (with some restrictions) if the base face is triangular (i.e., wedge, tetrahedron). Similarly, the w coordinate is between -1 and +1 if the height/depth face is quadrilateral (i.e., wedge, hexahedron), and between 0 and +1 if the height/depth face is triangular (i.e., pyramid, tetrahedron).

Note that the u and v values defined in the u-v-w system can be different to the u and v values on brick faces.

One use of these local coordinates if for the definition of the attachment points of nodes insides brick elements, such as might be required to attach a beam element to the inside of a brick element (see Insert: Attachment Link).

Tetrahedra

  Node Coordinates
u v w
1 0 0 0
2 1 0 0
3 0 1 0
4 0 0 1
5 0.5 0 0
6 0.5 0.5 0
7 0 0.5 0
8 0 0 0.5
9 0.5 0 0.5
10 0 0.5 0.5

 

Pyramids

  Node Coordinates
u v w
1 -1 -1 0
2 1 -1 0
3 1 1 0
4 -1 1 0
5 0 0 1
6 0 -1 0
7 1 0 0
8 0 1 0
9 -1 0 0
10 -0.5 -0.5 0.5
11 0.5 -0.5 0.5
12 0.5 0.5 0.5
13 -0.5 0.5 0.5

 

Wedges

  Node Coordinates
u v w
1 0 0 -1
2 1 0 -1
3 0 1 -1
4 0 0 1
5 1 0 1
6 0 1 1
7 0.5 0 -1
8 0.5 0.5 -1
9 0 0.5 -1
10 0 0 0
11 1 0 0
12 0 1 0
13 0.5 0 1
14 0.5 0.5 1
15 0 0.5 1

 

Hexahedra

  Node Coordinates
u v w
1 -1 -1 -1
2 1 -1 -1
3 1 1 -1
4 -1 1 -1
5 -1 -1 1
6 1 -1 1
7 1 1 1
8 -1 1 1
9 0 -1 -1
10 1 0 -1
11 0 1 -1
12 -1 0 -1
13 -1 -1 0
14 1 -1 0
15 1 1 0
16 -1 1 0
17 0 -1 1
18 1 0 1
19 0 1 1
20 -1 0 1

See Also