Skip to content

11. Coordinate system

Coordinate systems are specified using *CoordinateSystem. Each system must have a unique name, and duplicate names are not allowed. Coordinate systems are broadly categorized into user-defined systems with an origin (User) and systems without an origin, such as Orientation and Beam. The User coordinate system is used, for example, to define nodal coordinate systems. The Orientation system is used to apply local coordinate systems for elements, materials, loads, and boundary conditions. The Beam coordinate system is used to define element coordinate systems for beam elements.

*CoordinateSystem

Define a coordinate system.

*CoordinateSystem, TYPE=type Name=name
 ...
Keyword line
  • TYPE=type: Type of coordinate system
    • User: User coordinate system with an origin
    • Orientation: Originless coordinate system used for defining materials, loads, and boundary conditions
    • Beam: ECS of beam elements
  • Name=name: Name of the coordinate system

*CoordinateSystem, Type=User

Define user coordinate system with an origin

*CoordinateSystem, TYPE=User, Name=name
 axes1X,  axes1Y,  axes1Z
 axes2X,  axes2Y,  axes2Z
 originX, originY, originZ
First data line
  • axes1X, axes1Y, axes1Z: Direction vector of Axis 1 (X-axis) (required). It is converted into a unit vector.
Second data line
  • axes2X, axes2Y, axes2Z: Direction vector of Axis 2 (Y-axis) (required). Axis 3 is first computed from the given axes1 and axes2, then axes2 is recalculated and converted into a unit vector.
Third data line
  • originX, originY, originZ: Coordinate of origin [L].
Example
*CoordinateSystem, Name=XZ1
 1, 0, 0
 0, 0, 1
 0, 1, 0

*CoordinateSystem, Type=Orientation

Define originless coordinate system used for defining materials, loads, and boundary conditions

*CoordinateSystem, Type=Orientation, Name=name
 axes1X,  axes1Y,  axes1Z
 axes2X,  axes2Y,  axes2Z
First data line
  • axes1X, axes1Y, axes1Z: Direction vector of Axis 1 (X-axis) (required). It is converted into a unit vector.
Second data line
  • axes2X, axes2Y, axes2Z: Direction vector of Axis 2 (Y-axis) (required). Axis 3 is first computed from the given axes1 and axes2, then axes2 is recalculated and converted into a unit vector.

The coordinate system is defined as an orthogonal coordinate system based on the input coordinate system using the following equations.

\[ \small {\rm z} = {\rm x} \times {\rm y}, \quad {\rm y} = {\rm z} \times {\rm x} \]
Example
*CoordinateSystem, Type=Orientation, Name=INC30
  cos(30*pi/180), sin(30*pi/180), 0
  0,1,0

*CoordinateSystem, Type=Beam

Define ECS of beam elements

*CoordinateSystem, Type=Beam, Name=name
 angle, rx,ry,rz
First data line
  • angle: angle (unit: degree)(required)
  • rx,ry,rz: reference vector.(optional)
Example
*CoordinateSystem, Type=Beam, Name=beamcs
 90, 10.,0,0

*Element, Type=Beam3D
 1,1,2, S=beam, C=beamcs

*Distribution, Type=BeamCS
  slab, beamcs