HyperView Coordinate Systems

Subsequent options are dependent on the current averaging method. The available coordinate systems are:

Global

Element

Quad4/Quad8

For Quad elements, the reader automatically selects one of the following methods:

Figure 1. Method 1

• The origin of the coordinate system is located at the centroid of the element.
• x is along a line that bisects the angles between G2-G4 and G1-G3.
• y is perpendicular to x as shown in the figure.

Figure 2. Method 2

• The origin of the coordinate system is located at the centroid of the element.
• x is along the G1-G2 line.
• y is perpendicular to x.

Tria3/Tria6

Figure 3.

• The origin of the coordinate system is located at the centroid of the element.
• x is along the G1-G2 line.
• y is perpendicular to x as shown in the figure.

Hexa8/Hexa20

The element coordinate system for the Hexa element is defined in terms of the three vectors R, S, and T, which join the centroids of opposite faces, as follows:

• R vector joins the centroids of faces G4-G1-G5-G8 and G3-G2-G6-G7.
• S vector joins the centroids of faces G1-G2-G6-G5 and G4-G3-G7-G8.
• T vector joins the centroids of faces G1-G2-G3-G4 and G5-G6-G7-G8.

The origin of the coordinate system is located at the centroid of the element. The axes are derived as follows:

• z = T
• y = T x R
• x = y x z

Figure 4.

Tetra

The element coordinate system is derived from the three vectors, R, S, and T, which join the midpoints of opposite edges, as follows:

• R vector joins midpoints of edges G1-G2 and G3-G4.
• S vector joins midpoints of edges G1-G3 and G2-G4.
• T vector joins midpoints of edges G1-G4 and G2-G3.

The origin of the coordinate system is located at the centroid of the element. The axes are derived as follows:

• z = T
• y = T x R
• x = y x z

Figure 5.

Penta

The element coordinate system for the Penta element is derived accordingly. A midplane is formed by the three midpoints of the straight lines between the top (G1-G2-G3) and bottom (G4-G5-G6) triangular faces. The origin of the coordinate system is located at the centroid of the element. The axes are formed as follows:

• z = A line along the bisector of the midplane normal and the line connecting the centroids of the top (G1-G2-G3) and bottom (G4-G5-G6) faces.
• y = The vector connecting points P and Q where P and Q are defined as follows:

  P =	The midpoint along the line, G1-G4. In order to define Q, you must define a plane that passes through P and is perpendicular to axis z.
  Q =	The intersection of the plane defined above and the line G3-G6.

• x = The intersection of the plane defined above and the line G3-G6.

Figure 6.

Material

Ply

Analysis

User