2.1.5 Transformed coordinate systems

**Products: **ABAQUS/Standard ABAQUS/Explicit ABAQUS/CAE

A nodal transformation is used to define a local coordinate system for:

the definition of concentrated forces and moments;

the definition of displacement and rotation boundary conditions;

the definition of linear constraint equations; and

the output of vector-valued quantities in ABAQUS/Standard.

nodal coordinates—see “Specifying a local coordinate system in which to define nodes” in “Node definition,” Section 2.1.1, or “Specifying a local coordinate system for the nodal coordinates” in “Node definition,” Section 2.1.1, instead; or

material properties or rebars—see “Orientations,” Section 2.2.5, instead.

Defining a local coordinate system

Normally displacement and rotation components are associated with the global, rectangular Cartesian axis system. When a transformed coordinate system is associated with a node, all input data for concentrated forces and moments and for displacement and rotation boundary conditions at the node are given in the local system. The following transformations are available:

Rectangular Cartesian

Cylindrical

Spherical

Input File Usage: | You must identify the node set for which the local transformed system is defined. |

*TRANSFORM, NSET= |

ABAQUS/CAE Usage: | In ABAQUS/CAE you define a local coordinate system independent of its use and then refer to it when you apply a load or boundary condition at a node. |

Any module: Type: CSYSInteraction module: load or boundary condition editor: |

In a model defined in terms of an assembly of part instances, you can define a nodal transformation at the part, part instance, or assembly level. A nodal transformation defined at the part or part instance level will be rotated according to the positioning data given for each instance of that part (or for the part instance). See “Defining an assembly,” Section 2.9.1. Multiple transformation definitions are not allowed at a node, even if one of them is at the part level and another is at the assembly level.

The transformed coordinate system is always a set of fixed Cartesian axes at a node (even for cylindrical or spherical transforms). These transformed directions are fixed in space; the directions do not rotate as the node moves. Therefore, even in large-displacement analysis, the displacement components must always be given with respect to these fixed directions in space.

In a rectangular Cartesian transformation the transformed directions are parallel at all nodes of the set. The coordinates of two points must be given, as shown in Figure 2.1.5–1.

The first point, *a*, must be on a line through the global origin; this point defines the transformed -direction. The second point, *b*, must be in the plane containing the global origin and the transformed - and -directions. This second point should be on or near the positive -axis.

Input File Usage: | *TRANSFORM, NSET= |

ABAQUS/CAE Usage: | Any module: Type: CSYS: select any method, and click OK: Rectangular |

The radial, tangential, and axial directions must be defined based on the original coordinates of each node in the node set for which the transformation is invoked. The global () coordinates of the two points defining the axis of the cylindrical system (points *a* and *b* as shown in Figure 2.1.5–2) must be given.

The origin of the local coordinate system is at the node of interest. The local -axis is defined by a line through the node, perpendicular to the line through points *a* and *b*. The local -axis is defined by a line that is parallel to the line through points *a* and *b*. The local -axis forms a right-handed coordinate system with and .

A cylindrical coordinate system cannot be defined for a node that lies along the line joining points *a* and *b*.

Input File Usage: | *TRANSFORM, NSET= |

ABAQUS/CAE Usage: | Any module: Type: CSYS: select any method, and click OK: Cylindrical |

The radial, circumferential, and meridional directions must be defined based on the original coordinates of each node in the node set for which the transformation is invoked. The global () coordinates of the center of the spherical system, *a*, and of a point on the polar axis, *b*, must be given as shown in Figure 2.1.5–3.

The origin of the local coordinate system is at the node of interest. The local -axis is defined by a line through the node and point *a*. The local -axis lies in a plane containing the polar axis (the line between points *a* and *b*) and is perpendicular to the local -axis. The local -axis forms a right-handed coordinate system with and .

A spherical coordinate system cannot be defined for a node that lies along the line joining points *a* and *b*.

Input File Usage: | *TRANSFORM, NSET= |

ABAQUS/CAE Usage: | Any module: Type: CSYS: select any method, and click OK: Spherical |

Output at a node associated with a coordinate transformation

Printed and file output of vector-valued quantities from ABAQUS/Standard at transformed nodes can be in the local or global system (see “Specifying the directions for nodal output” in “Output to the data and results files,” Section 4.1.2). By default, the values are written to the data file in the local system, whereas the values are written to the results file in the global system (since this is more convenient for postprocessing). Consequently, reaction forces printed using the default will not appear to equilibrate loads applied in the global system. However, these reaction forces and loads should equilibrate if you output them to the data file in the global system.

File output from ABAQUS/Explicit is always in the global system.

Output database output of vector-valued quantities at transformed nodes is in the global system. The local transformations are also written to the output database. You can apply these transformations to the results in the Visualization module of ABAQUS/CAE to view the vector components in the transformed systems.