Generate Cylindrical Structure (GR)

Purpose:  To reproduce a structure while rotating about the Z-axis to form a
          complete cylindrical array and to set flags so that symmetry is
          utilized in the solution.

Card:
           Cols  Parameter
          ----------------
           1- 2  GR
           3- 5  I1
           6-10  I2
          11-20  blank
          21-30  blank
          31-40  blank
          41-50  blank
          51-60  blank
          61-70  blank
          71-80  blank

Parameters:
        Integers
           (I1) - Tag number increment.
           (I2) - Total number of times that the structure is to occur in the
                  cylindrical array.

        Decimal Numbers
           The decimal number fields are not used.

Notes:
• The tag increment (I1) is used to avoid duplication of tag numbers in the reproduced structures. In forming a new structure for the array, all valid tags on the previous copy or original structure are incremented by (I1). Tags equal to zero are not incremented.
• The GR card should never be used when there are segments on the Z-axis or crossing the Z-axis since overlapping segments would result.
• The GR card sets flags so the program makes use of cylindrical symmetry in solving for the currents. If a structure modeled by N segments has M sections in cylindrical symmetry (formed by a GR card with I2 equal to M), the number of complex numbers in matrix storage and the proportionality factors for matrix fill time and matrix factor time are:

                                     Matrix         Fill        Factor
                                    Storage         Time         Time
                                    -------         ----        ------
  
           No Symmetry                N^2            N^2         N^2
  
           M Symmetric Sections      (N^2)/M        (N^2)/M     (N^2)/M
  

  The matrix factor time represents the optimum for a large matrix factored in core. Generally, somewhat longer times will be observed.
• If the structure is added to or modified after the GR card in such a way that cylindrical symmetry is destroyed, the program must be reset to a no-symmetry condition. In most cases, the program is set by the geometry routines for the existing symmetry. Operations that auto- matically reset the symmetry conditions are:
  • Addition of a wire by a GW card destroys all symmetry.
  • Generation of additional structures by a GM card, with NRPT greater than zero, destroys all symmetry.
  • A GM card acting on only part of the structure (having ITS greater than zero) destroys all symmetry.
  • A GX or GR card will destroy all previously established symmetry.
  • If a structure is rotated about either the X or Y axis by use of a GM card and a ground plane is specified on the GE card, all symmetry will be destroyed. Rotation about the Z-axis or transla- tion will not affect symmetry. If a ground is not specified, symmetry will be unaffected by any rotation or translation by a GM card, unless NRPT or ITS on the GM card is greater than zero.
• Symmetry will also be destroyed if lumped loads are placed on the struc- ture in an unsymmetric manner. In this case, the program is not auto- matically set to a no-symmetry condition but must be set by a data card following the GR card. A GW card with NS blank will set the program to a no-symmetry condition without modifying the structure. The card must specify a nonzero radius, however, to avoid reading a GC card.
• Placement of nonradiating networks or sources does not affect symmetry.
• When symmetry is used in the solution, the number of symmetric sections (I2) is limited by array dimensions. In the demonstration deck, the limit is 16 sections.
• The GR card produces the same effect on the structure as a GM card if I2 on the GR card is equal to (NRPT+1) on the GM card and if ROZ on the GM card is equal to 360/(NRPT+1) degrees. If the GM card is used, however, the program will not be set to take advantage of symmetry.

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