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3.1 Types of Coordinate Systems
The ANSYS program has several types of coordinate systems, each used for a
different reason:
- Global and local coordinate systems are used to locate geometry items
(nodes, keypoints, etc.) in space.
- The display coordinate system determines the system in which geometry
items are listed or displayed.
- The nodal coordinate system defines the degree of freedom directions at
each node and the orientation of nodal results data.
- The element coordinate system determines the orientation of material
properties and element results data.
- The results coordinate system is used to transform nodal or element results
data to a particular coordinate system for listings, displays, or general
postprocessing operations (POST1).
The working plane, which is separate from the coordinate systems discussed in
this chapter, is used to locate geometric primitives during the modeling process.
See Chapter 4 for more information about the working plane.
3.2 Global and Local Coordinate Systems
Global and local coordinate systems are used to locate geometry items. By
default, when you define a node or a keypoint, its coordinates are interpreted in
the global Cartesian system. For some models, however, it may be more
convenient to define the coordinates in a system other than global Cartesian. The
ANSYS program allows you to input the geometry in any of three predefined
(global) coordinate systems, or in any number of user defined (local) coordinate
systems.
3.2.1 Global Coordinate Systems
A global coordinate system can be thought of as an absolute reference frame.
The ANSYS program provides three predefined global systems: Cartesian,
cylindrical, and spherical. All three of these systems are right-handed and, by
definition, share the same origin. They are identified by their coordinate system
(C.S.) numbers: 0 for Cartesian, 1 for cylindrical, and 2 for spherical. (See Figure
3-1.)
Figure 3-1 Global coordinate systems
3.2.2 Local Coordinate Systems
In many cases, it may be necessary to establish your own coordinate system,
whose origin is offset from the global origin, or whose orientation differs from that
of the predefined global systems. (See Figure 3-2 for an example of a coordinate
system defined by rotations.) Such user defined coordinate systems, known as
local coordinate systems, can be created in the following ways:
- Define the local system in terms of global Cartesian coordinates.
Command(s):
GUI:
Utility Menu>WorkPlane>Local Coordinate Systems>Create Local CS>
At Specified Loc
- Define the local system in terms of existing nodes.
Command(s):
GUI:
Utility Menu>WorkPlane>Local Coordinate Systems>Create Local CS>
By 3 Nodes
- Define the local system in terms of existing keypoints.
Command(s):
GUI:
Utility Menu>WorkPlane>Local Coordinate Systems>Create Local CS>
By 3 Keypoints
- Define the local system to be centered at the origin of the presently defined
working plane.
Command(s):
GUI:
Utility Menu>WorkPlane>Local Coordinate Systems>Create Local CS>
At WP Origin
- Define the local system in terms of the active coordinate system with the
CLOCAL command (see the later
section titled "The Active Coordinate System"). (There is no GUI equivalent
for the CLOCAL command.)
When a local coordinate system is defined, it becomes the active coordinate
system. As you create a local system, you assign it a C.S. identification number
(which must be 11 or greater). You can create (or delete) local coordinate
systems in any phase of your ANSYS session. To delete a local system, use one
of the following methods:
Command(s):
GUI:
Utility Menu>WorkPlane>Local Coordinate Systems>Delete Local CS
To view the status of all global and local coordinate systems, use one of the
following methods:
Command(s):
GUI:
Utility Menu>List>Other>Local Coord Sys
Your local coordinate systems can be Cartesian, cylindrical, or spherical, similar in
form to the three predefined global systems. Note that you may define local
cylindrical and spherical coordinate systems in either circular or elliptical
configuration. Additionally, you can define a toroidal local coordinate system, as
illustrated in Figure 3-3.
Note-Solid modeling operations in a toroidal coordinate system are not
recommended. Areas or volumes generated may not be what you expect.
Figure 3-2 Euler rotation angles used for local, nodal, or working plane
coordinate system rotations
Figure 3-3 Coordinate system types
3.2.3 The Active Coordinate System
You may define as many coordinate systems as you like, but only one of these
systems may be active at a time. The choice of active coordinate system is
determined as follows: Initially, the global Cartesian system is active by default.
Each time you define a local coordinate system, that newly-defined system then
automatically becomes the active one. If you want to activate one of the global
coordinate systems or some other previously defined coordinate system, use one
of the following methods:
Command(s):
GUI:
Utility Menu>Change Active CS to>Global Cartesian
Utility Menu>Change Active CS to>Global Cylindrical
Utility Menu>Change Active CS to>Global Spherical
Utility Menu>Change Active CS to>Specified Coord Sys
Utility Menu>Change Active CS to>Working Plane
You can activate a coordinate system in any phase of your ANSYS session. That
same coordinate system will remain active in all subsequent phases until you
change it explicitly.
Note-When you define a keypoint or a node, the program response labels the
coordinates as X, Y, and Z, regardless of which coordinate system is active. You
should make the appropriate mental substitutions if the active coordinate system
is not Cartesian (R,
,Z for cylindrical and R,,
for spherical or toroidal).
Specifying a constant value for a single coordinate implies a surface. For
example, X=3 represents the Y-Z plane (or surface) at X=3 in a Cartesian system.
Implied surfaces are used with various operations, such as selecting (xSEL
commands) and moving (MOVE, KMOVE, etc.) entities. Some surfaces of
constant value (C) are illustrated in Figure 3-4 and Figure 3-5. These surfaces
may be located in either global or local coordinate systems to allow for any
desired orientation. Note that for surfaces in elliptical coordinate systems, a
constant R value (R=C) represents the value of R along the X-axis.
Figure 3-4 Some surfaces of constant value
Figure 3-5 Some surfaces of constant value
3.2.5 Closed Surfaces and Surface Singularities
Open surfaces are assumed to be infinite. Cylindrical circular surfaces have a
singularity at = " 180°, as shown in Figure 3-6, so that a fill generation of a
string of nodes [FILL] or keypoints [KFILL] does not cross the 180° line. A fill
operation defined from A to C will pass through B. A fill operation from A to D will
pass through E. A fill operation from C to D will pass through B, A, and E.
For a specified cylindrical coordinate system, you can move the singularity point to
=0° (or 360°) so that a fill operation from C to D will not pass through B, A, or E.
To move the singularity point, use one of the following methods:
Command(s):
GUI:
Utility Menu>WorkPlane>Local Coordinate Systems>Move Singularity
Figure 3-6 Singularity points
A similar singularity occurs in the toroidal coordinate system at 
= "180° and
can also be moved by the above methods. Singularities also occur in the
spherical coordinate system at = "90°, such that these locations should not be
used.
Note that solid model lines will not be affected by these singularity locations. A
curved line between two keypoints will take the shortest path in the angular
direction, without regard to the location of the singularity point. (As a result,
curved lines cannot span an arc of more than 180°.) Thus, in the figure above,
circular lines from B to D or from D to B will pass through C.
3.3 Display Coordinate System
By default, a listing of nodes or keypoints always shows their global Cartesian
coordinates, even if they were defined in a different coordinate system. You can
change the display coordinate system used in such listings by one of the following
methods:
Command(s):
GUI:
Utility Menu>WorkPlane>Change Display CS to>Global Cartesian
Utility Menu>WorkPlane>Change Display CS to>Global Cylindrical
Utility Menu>WorkPlane>Change Display CS to>Global Spherical
Utility Menu>WorkPlane>Change Display CS to>Specified Coord Sys
Changing the display coordinate system will also affect your graphical displays.
Unless you desire a specific effect in your displays, you should usually reset the
display coordinate system to C.S. 0 (the global Cartesian system) before issuing
any graphics display action commands (such as NPLOT, EPLOT, etc.). (Line plots [LPLOT], area plots [APLOT], and volume plots [VPLOT] are not affected by DSYS.)
3.4 Nodal Coordinate Systems
While global and local coordinate systems locate geometry items, the nodal
coordinate system orients the degree of freedom directions at each node. Each
node has its own nodal coordinate system, which, by default, is parallel to global
Cartesian (regardless of the active coordinate system in which the node was
defined). You can rotate the nodal coordinate system at any node to a desired
orientation using one of the following methods:
- Rotate the nodal coordinate system into the active coordinate system. That
is, the nodal X-axis is rotated to be parallel to the X or R axis of the active
system, the nodal Y-axis is rotated to be parallel to the Y or axis of the
active system, and the nodal Z-axis is rotated to be parallel to the Z or
axis of the active system.
Command(s):
GUI:
Main Menu>Preprocessor>Create>Nodes>-Rotate Node CS
-To Active CS
Main Menu>Preprocessor>Move/Modify>-Rotate Node CS
-To Active CS
- Rotate the nodal coordinate system by known rotation angles. (Since you
will usually not know these rotation angles explicitly, you will probably find
the NROTAT method to be more
useful.) You can define the rotation angles at the time the node is created
[N], or you can specify rotation angles for
existing nodes [NMODIF].
Command(s):
GUI:
Main Menu>Preprocessor>Create>Nodes>In Active CS
Command(s):
GUI:
Main Menu>Preprocessor>Create>Nodes>-Rotate Node CS
-By Angles
Main Menu>Preprocessor>Move/Modify>-Rotate Node CS-By Angles
- Rotate the nodal coordinate system by direction cosine components.
Command(s):
GUI:
Main Menu>Preprocessor>Create>Nodes>-Rotate Node CS
- By Vectors
Main Menu>Preprocessor>Move/Modify>-Rotate Node CS
-By Vectors
You can list the nodal coordinate rotation angles with respect to the global
Cartesian system using one of the following methods:
Command(s):
GUI:
Utility Menu>List>Nodes
Utility Menu>List>Picked Entities>Nodes
Figure 3-7 Nodal coordinate systems
3.4.1 Data Interpreted in the Nodal Coordinate System
Input data that are interpreted in the nodal coordinate system include component
values of the following:
degree of freedom constraints
forces
master DOF
coupled nodes
constraint equations
The following results data are reported in the nodal coordinate system on the
output file and in POST26:
degree of freedom solution
nodal loads
reaction loads
In POST1, results data are reported in terms of the results coordinate system [RSYS], not the nodal coordinate system.
3.5 Element Coordinate Systems
Every element has its own coordinate system, the element coordinate system,
that determines the direction of orthotropic material properties, applied pressures,
and results (such as stresses and strains) for that element. All element
coordinate systems are right-handed orthogonal systems.
The default orientations for most elements' coordinate systems fit the following
patterns:
- Line elements usually have the element X-axis directed from their node I
toward their node J.
- Shell elements usually have the element X-axis similarly directed (from I
toward J), the Z-axis normal to the shell surface (with the positive direction
determined by the right-hand rule around the element from node I to J to
K), and the Y-axis perpendicular to the X and Z axes.
- For 2-D and 3-D solid elements, the element coordinate system is usually
parallel to the global Cartesian system.
However, not all elements correspond to these patterns; see specific element
descriptions in the ANSYS Elements Reference
for the default element coordinate system orientation for such elements.
Many element types have key options (KEYOPTs; input at the time the element is
defined [ET] or on the KEYOPT command) that allow you to
change the default element coordinate system orientation. For area and volume
elements, you can also change the orientation to align the element coordinate
system with a previously defined local system by using one of the following
methods:
Command(s):
GUI:
Main Menu>Preprocessor>-Attributes-Define>Default Attribs
Main Menu>Preprocessor>Create>Elements>Elem Attributes
If you specify both KEYOPTs and ESYS, the
ESYS definition overrides. For some
elements, you can define a further rotation, relative to the previous orientation, by
entering an angle as a real constant. (See, for example, the real constant THETA
in the SHELL63 description.)
3.6 The Results Coordinate System
Results data are calculated during solution and consist of displacements (UX, UY,
ROTX, etc.), gradients (TGX, TGY, etc.), stresses (SX, SY, SZ, etc.), strains
(EPPLX, EPPLXY, etc.), etc. These data are stored in the database and on the
results file in either the nodal coordinate system (for the primary, or nodal data) or
the element coordinate system (for the derived, or element data). However,
results data are generally rotated into the active results coordinate system (which
is by default the global Cartesian system) for displays, listings, and element table
data storage [ETABLE].
You can change the active results coordinate system to another system (such as
the global cylindrical system or a local coordinate system), or to the coordinate
systems used during solution (i.e., the nodal and element coordinate systems). If
you then list, display, or operate on the results data, they are rotated to this results
coordinate system first. Use one of the following methods to change the results
coordinate system:
Command(s):
GUI:
Main Menu>General Postproc>Options for Output
Utility Menu>List>Results>Options
See Chapter 5 of the ANSYS Basic Analysis
Procedures Guide for details on rotating results to a different coordinate
system for postprocessing.
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