4.1          Cartesian Coordinates Generation

 

4.1.1       Cartesian Nodal Coordinate Data

 

Note             Variable        Default                  Description

 

(1)                     N                 [0]                      Node number  1 and  NUMNP

 

(2)               NUMGP           [0]                      Number of generation points  0

                                                                           = 0, no generation

                                                                           > 0, generate data

 

                     X(1, N)           [0.0]                    X1-coordinate of node N

 

                     X(2, N)           [0.0]                    X2-coordinate of node N

 

                     X(3, N)           [0.0]                    X3-coordinate of node N

 

 

Notes/

(1)        The coordinates of each node must be defined, but need not be read in order. If the coordinates of node N are input and/or generated more than one time, the last values take priority.  Terminate with a blank record.

 

(2)        If NUMGP is greater than zero, this record initiates an isoparametric data generation sequence.  Records 2 to NUMGP of the sequence define the coordinates of the additional generation points (see Section 4.1.2).  The final record of the sequence defines the nodal increment information (see Section 4.1.3).  After the generation sequence is completed, additional nodal coordinate records, or generation sequences, may follow.

 

            The generation may be performed along a line, over a surface, or over a volume.  A description of each of these options is given hereafter.

 

 

A. Generation Along a Line

 

            The line may be defined by 2, or 3, generation points (see Figure 4.1.1), and the physical space may be 1, 2, or 3 dimensional.

 

            In the case NUMGP = 2, linear interpolation takes place resulting in equally spaced nodal points.

 

            In the case NUMGP = 3, quadratic interpolation is employed and graded nodal spacing may be achieved by placing the third generation point (J = 3) off center.  Note that the third generation point does not generally coincide with any nodal point.  The spacing in this case may be determined from the following mapping:

 

 

where  is the location of node number A in -space (the nodes are placed at equal intervals in -space); x1g, x2g and x3g are the coordinates of the three generation points in x-space; and xA denotes the coordinates of the Ath node in x-space (see Figure 4.1.2).

 

B. Generation Over a Surface

 

            The surface may be defined by 4, or 8, generation points (see Figure 4.1.3) and the physical space may be 2, or 3 dimensional.  In the 3-dimensional case, the surfaces may be curved.

 

            In the case NUMGP = 4, bilinear interpolation is employed, resulting in equally spaced nodal points along generating lines.

 

            In the case NUMGP = 8, biquadratic "serendipity" interpolation is employed and graded nodal spacing may be achieved by placing generation point 5-8 off center.  Note that generation points 5-8 do not generally coincide with any nodal points.  The spacing of the nodal points may be determined from the serendipity mapping.

 

C. Generation Over a Volume

 

            The volume is brick shaped and may be defined by 8, or 20, generation points (see Figure 4. 1.4).  In this case the physical space must be 3-dimensional.

 

            If NUMGP = 8, trilinear interpolation is employed, resulting in equally spaced nodal points along generating lines.

 

            If NUMGP = 20, triquadratic serendipity interpolation is employed and graded nodal spacing may be achieved by placing generation points 9-20 off center.  Note that generation points 9-20 do not generally coincide with any nodal points.  The spacing of the nodal points may be determined by the serendipity mapping.

 

 

4.1.2       Generation Point Coordinate Data (NUMGP-1)

 

            The coordinates of each generation point are defined by a generation point coordinate record.  The records must be read in order (J = 2, 3,..., NUMGP) following the nodal coordinate record which initiated the generation sequence (J = 1).  A nodal record (see Section 4.1.3), which completes the sequence, must follow the last generation point record.

 

Note        Variable       Default            Description

 

                     M                [0]                Node number

 

                 MGEN           [0]                Generation parameter

                                                            = 0, coordinates of the Jth generation point are input on
                                                                 this record; M is ignored.

                                                            = 1, coordinates of the Jth generation point are set equal to
                                                                 coordinates of node M which was previously defined;
                                                                 coordinates on this record are ignored

 

             TEMP(1, J)       [0.0]              X1-coordinate of generation point J

 

             TEMP(2, J)       [0.0]              X2-coordinate of generation point J

 

             TEMP(3, J)       [0.0]              X3-coordinate of generation point J

 

 

 

4.1.3       Nodal Increments Data

 

Note             Variable           Default               Description

 

                     NINC(1)             [0]                   Number of nodal increments for direction 1

 

                       INC(1)              [0]                   Node number increment for direction 1

 

(1)                 NINC(2)             [0]                   Number of nodal increments for direction 2

 

                       INC(2)              [0]                   Node number increment for direction 2

 

(1)                 NINC(3)             [0]                   Number of nodal increments for direction 3

 

                       INC(3)              [0]                   Node number increment for direction 3

 

 

Notes/

(1)        Each option is assigned an option code (IOPT) as follows:

                                    IOPT           Option

                                        1             Generation along a line

                                        2             Generation over a surface

                                        3             Generation over a volume

            IOPT is determined by the following logic:

                                    IOPT = 3

                                    IF(NINC(3) = 0)   IOPT = 2

                                    IF(NINC(2) = 0)   IOPT = 1

 

 

 

 

Figure 4.1.1  Nodal Generation Along a Line

 

 

 

 

 

Figure 4.1.2  Nodal Generation Along a Line:  Mapping from Local Interval to Physical Space

 

 

 

Figure 4.1.3  Nodal Generation Over a Surface

 

 

 

Figure 4.1.4  Nodal Generation Within a Volume

 

 

Notes . .