abaqus建模中映射节点的方法

Mapping a set of nodes from one coordinate system to another

You can map a set of nodes from one coordinate system to another. You can also rotate, translate, or scale the nodes in a set by using a more direct method instead of coordinate system mapping. These capabilities are useful for many geometric situations: a mesh can be generated quite easily in a local coordinate system (for example, on the surface of a cylinder) using other methods and then can be mapped into the global (X, Y, Z) system. In other cases some parts of your model need to be translated or rotated along a given axis or scaled with respect to one point.

The mapping capability cannot be used in a model defined in terms of an assembly of part instances.

The following different mappings are provided: a simple scaling; a simple shift and/or rotation; skewed Cartesian; cylindrical; spherical; toroidal; and, in Abaqus/Standard only, blended quadratic. The first five of these mappings are shown in Figure 2.1.1–13.

Figure 2.1.1–13 Coordinate systems; angles are in degrees.

Blended quadratic mapping is shown in Figure 2.1.1–14.

Figure 2.1.1–14 Use of blended quadratic mapping to develop a solid mesh onto a curved block.

In all cases the coordinates of the nodes in the set are assumed to be defined in the local system: these local coordinates at each node are replaced with the global Cartesian (X, Y, Z) coordinates defined by the mapping. All angular coordinates should be given in degrees.

You can use either coordinates or node numbers to define the new coordinate system, the axis of rotation and translation, or the reference point used for scaling.

The mapping capability can be used several times in succession on the same nodes, if required.

Scaling the local coordinates before they are mapped

For all mappings except the blended quadratic mapping, you can specify a scaling factor to be applied to the local coordinates before they are mapped.

This facility is useful for “stretching” some of the coordinates that are given. For example, in cases where the local system uses some angular coordinates and some distance coordinates (cylindrical, spherical, etc.), it may be preferable to generate the mesh in a system that uses distance measures in the angular directions and then scale onto the angular coordinate system for the mapping.

Two different scaling methods are available.

Specifying the scaling factors directly

A first method of scaling the nodes with respect to the origin of the local system is to specify the scale factors directly. In this case the scaling is done at the same time as the mapping from one coordinate system to another.

Input File Usage: *NMAP, NSET=name

first data line second data line

scale factor for first local coord, scale factor for second local coord, scale factor for third local coord

Specifying the scaling with respect to a reference point

Alternatively, you can scale with respect to a point other than the origin. The reference point with respect to which the scaling is done can be defined by using either its coordinates or the user node number. Input File Usage: Use the following option to define the

scaling reference point by using its coordinates (default):

*NMAP, TYPE=SCALE, DEFINITION=COORDINATES

X-coordinate of reference point, Y-coordinate of reference point, Z-coordinate of reference point

scale factor for first local coord, scale factor for second local coord, scale factor for third local coord

Use the following option to define the scaling reference point by using its node number:

*NMAP, TYPE=SCALE, DEFINITION=NODES

Local node number of the reference point scale factor for first local coord, scale factor for second local coord, scale factor for third local coord

Introducing a simple shift and/or rotation by mapping from one coordinate system to another

In the case of a simple shift and/or rotation, point a in Figure 2.1.1–13 defines the origin of the local rectangular coordinate system defining the map. The local -axis is defined by the line joining points a and b. The local – plane is defined by the plane passing through points a, b, and c.

Input File Usage: *NMAP, NSET=name, TYPE=RECTANGULAR

Introducing a pure shift by specifying the axis and magnitude of the translation

You can define a pure translation (or shift) to move a set of nodes by a prescribed value along a desired axis. You must specify the axis of translation by providing either the coordinates or the two node numbers defining this axis, and you must prescribe the magnitude of the translation.

Input File Usage: Use the following option to specify the axis

of translation using coordinates (default): *NMAP, NSET=name, TYPE=TRANSLATION, DEFINITION=COORDINATES

Use the following option to specify the axis of translation using node numbers: *NMAP, NSET=name, TYPE=TRANSLATION, DEFINITION=NODES

Introducing a pure rotation by specifying the axis, origin, and angle of the rotation

You can define a rotation of a set of nodes by providing the axis of rotation, the origin of rotation, and the magnitude of the rotation. You must specify the axis of rotation by providing either the coordinates or the two node numbers defining this axis. You must specify the origin of the rotation by providing either the coordinates or the node number at the origin of rotation. Finally, you must specify the angle of the rotation in degrees.

Input File Usage: Use the following option to specify the axis

of rotation using coordinates (default): *NMAP, NSET=name, TYPE=ROTATION, DEFINITION=COORDINATES

Use the following option to specify the axis of rotation using node numbers: *NMAP, NSET=name, TYPE=ROTATION, DEFINITION=NODES

Mapping from cylindrical coordinates

For mapping from cylindrical coordinates, point a in Figure 2.1.1–13 defines the origin of the local cylindrical coordinate system defining the map. The line going through point a and point b defines the -axis of the local cylindrical coordinate system. The local – plane for

is defined by the plane passing through points a, b, and c. Input File Usage: *NMAP, NSET=name, TYPE=CYLINDRICAL

Mapping from skewed Cartesian coordinates

For mapping from skewed Cartesian coordinates, point a in Figure 2.1.1–13 defines the origin of the local diamond coordinate system defining the map. The line going through point a and point b defines the -axis of the local coordinate system. The line going through point a and point c

defines the -axis of the local coordinate system. The line going through point a and point d defines the -axis of the local coordinate system. Input File Usage: *NMAP, NSET=name, TYPE=DIAMOND

Mapping from spherical coordinates

For mapping from spherical coordinates, point a in Figure 2.1.1–13 defines the origin of the local spherical coordinate system defining the map. The line going through point a and point b defines the polar axis of the local spherical coordinate system. The plane passing through point a and perpendicular to the polar axis defines the plane. The plane passing through points a, b, and c defines the local plane. Input File Usage: *NMAP, NSET=name, TYPE=SPHERICAL

Mapping from toroidal coordinates

For mapping from toroidal coordinates, point a in Figure 2.1.1–13 defines the origin of the local toroidal coordinate system defining the map. The axis of the local toroidal system lies in the plane defined by points a, b, and c. The R-coordinate of the toroidal system is defined by the distance between points a and b. The line between points a and b defines the position. For every value of the -coordinate is defined in a plane perpendicular to the plane defined by the points a, b, and c and perpendicular to the axis of the toroidal system. lies in the plane defined by the points a, b, and c.

Input File Usage: *NMAP, NSET=name, TYPE=TOROIDAL

Mapping by means of blended quadratics

To map by means of blended quadratics in Abaqus/Standard, you define the new (mapped) coordinates of up to 20 “control nodes”: these are the corner and midedge nodes of the block of nodes being mapped. The mapping in this case is like that of a 20-node brick isoparametric element. Any of the midedge nodes can be omitted, thus allowing linear interpolation along that edge of the block. Abaqus/Standard does not check whether the nodes in the set lie within the physical space of the block defined by

the corner and midedge nodes: these control nodes simply define mapping functions that are then applied to all of the nodes in the set. The control nodes should define a “well”-shaped block; for example, midedge nodes should be close to the midpoint of the edge. Otherwise, the mapping can be very distorted. For example, the nodes of a crack-tip 20-node element with midside nodes at the quarter points will not map correctly and, therefore, should not be used as the control nodes. Blended mapping is only available for three-dimensional analyses. Input File Usage: *NMAP, NSET=name, TYPE=BLENDED

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