X.B.4.1 Local coordinate systems

Several types of local coordinate systems may be defined, and the operations performed to define the coordinate system depend on the case:

1.

The “elemIJK” coordinate system definitions may be found in Patran User Manual. It is also common to the element coordinate systems of most finite element programs. Usually, it is defined with the three first definition nodes of the element. Direction X corresponds to the vector from node 1 to node 3. Direction Y is determined from the position of node 3.

2.

The “plyCS” coordinate system is obtained on surfacic elements with “PCOMP” or “PCOMPG” properties by rotating the local material coordinate system with the appropriate angle around its axis Z. For other elements, the ”plyCS” coordinate system is identical to the material coordinate system.

3.

The “matCS” coordinate system definition depends on the type of element:

(a)

For 0D elements, no material coordinate system exists.

(b)

For 1D elements, the material coordinate system corresponds the element coordinate systems (i.e. Nastran element coordinate system).

(c)

For 2D elements, the material coordinate system can be defined by two methods:

i.

If the material coordinate system is defined by an integer, this integer corresponds to the index of the coordinate system defined in the DataBase. Then the new coordinate system as follows:

• The First vector of the coordinate system is extracted.
• It is projected on the XY plane defined by the Nastran element coordinate system. This gives the vector X of the local material Cartesian coordinate system.
• The Vector Z of the local material Cartesian coordinate system is identical to the vector Z of Nastran element coordinate system.

ii.

if the material coordinate system is defined by a real argument, the value corresponds to a rotation angle $\theta$. Then the local material Cartesian coordinate system is defined as follows:

• One first builds the IJK Cartesian coordinate system.
• Then the vector X of IJK coordinate system is rotated by an angle $\theta$ around axis $Z$ of IJK coordinate system.
• This rotated vector s projected on the XY plane defined by the Nastran element coordinate system. This gives the vector X of the local material Cartesian coordinate system.
• The Vector Z of the local material Cartesian coordinate system is identical to the vector Z of Nastran element coordinate system.

(d)

For 3D elements, the material coordinate is generally identified by an integer in the “PSOLID” card. It is then retrieved from the DataBase. If no material coordinate system is specified in the “PSOLID” card, then the material coordinate system corresponds to the Nastran element coordinate system.

4.

The “nodeCS” coordinate system corresponds to the node analysis coordinate system. See Nastran reference guide for more information.

5.

The “elemCS” coordinate system corresponds to the Nastran local coordinate system. See Nastran reference guide for more information. Note that the construction of Nastran local coordinate system for CQUAD and 3D elements is complicated. (See sections X.B.4.4 and X.B.4.5 for more information.)