Card 9 - INTERP Interpolation Definition

This optional card defines the interpolation of a variable applied to an element, group, or conductance number.

Parameters: KODE, N1, T1, T2, T3, T4, T5, T6

KODE

KODE in the code INTERP (or 7)

N1

N1 is the element number, group name, or conductance number of the dependent variable. The interpolated variable is applied on N1.

If N1 is a group name, the interpolated variable is applied on all the elements of the group, and T1 should be 0.

T1

T1 is the element number, group name, or conductance number of the independent variable.

If T1 is a group name, the value of the independent variable is averaged over the elements of that group.

T1 = 0 defaults to T1 = N1.

T2

T2 is a table or expression number.

T3

T3 may be a multiplying factor for the interpolated variable. The dependent variable Y(I) at element I is computed by interpolation from the table T2 by:

where:

  • Y(I) is the computed dependent variable at element I
  • X(T1,I) is the independent variable at elements I and T1
  • I is an element number that is part of the group N1
  • Ω(T2) represents the result of the interpolation procedure over table T2

T3 = AREA (or 1E36), in which case the interpolated variable Y(I) is multiplied by the area of I.

T3 = VOLUME (or 3E36), in which case the interpolated variable Y(I) is multiplied by the volume of I. For planar and beam elements, the volume is calculated by multiplying the length or area by the cross-sectional area or thickness.

T3 = TOTAL (or 2E36), in which case the interpolated variable (e.g. heat load) is redistributed among the elements of group N1 in proportion to their areas or volumes.

where:

  • AV(I) is either the volume (for solid elements) or area of element I (for shells and beams), or unity (for non-dimensional element), where I is a member of the N1 group. For the TOTAL option all the elements of group N1 must be of the same type, i.e. solid and non-solid elements may not be mixed.

If table T2 is a spatial table (field or EID dependent), then Y(I) is calculated with a weighting factor Ω(I) interpolated from this table:

T4

T4 is a multiplying factor for the interpolated variable, effective only if T3 = AREA, VOLUME, or TOTAL. For all other options it defaults to 1.

T5

T5 specifies the layer for multilayer elements:

  • 0 or blank indicates that the element is not a multilayer. For non-uniform multilayers, T5 = 0 or blank is identical to T5 = TOP. For uniform multilayers, T5 = 0 or blank is identical to T5 = MIDDLE.
  • TOP indicates that heat load is applied to the top layer.
  • MIDDLE indicates that the heat load is applied to the middle layer.
  • BOTTOM indicates that the heat load is applied to the bottom layer.
  • ALL indicates that the heat load is applied to all layers.
  • SPECIFY or FROMBOT indicates that the heat load is applied to the T6th layer.

T6

T6 is the layer number counted from the bottom layer of the multilayer. It is only used if T5 = SPECIFY or FROMBOT.

Code example


INTERP 2 1 3 3.0 
TABTYPE 3 QNODE TEMP 
TABDATA 3 2 4
TABDATA 3 8 10
$ INTERPOLATES HEAT LOAD TO ELEMENT 2 AS A FUNCTION
$ OF TEMP OF ELEMENT 1. FOR A TEMP OF 7.0 THE
$ CALCULATED HEAT LOAD = 15
$ = 3*((7-4)/(10-4)*(8-2)+2)

Notes

The value of the dependent variable is calculated by linear table interpolation at each Analyzer iteration or time step and multiplied by T3 or T4.

Table T2 is defined with TABTYPE or FIELDTYPE Cards. TABTYPE and FIELDTYPE Cards define the type of the independent and dependent variables. TABDATA and FIELDDATA Cards contain the table data. Alternatively, T2 may reference a bivariate array defined by ARRAYTYPE and ARRAYDATA Cards.

A conductance-dependent variable Y(N1) is evaluated differently from the above procedure:

where:

  • GORIG is the conductance parameter calculated from geometry by the COND, GRAYB, or VUFAC modules, or created with XCOND Cards.
  • N1 is the conductance number. The conductance number may be specified on XCOND Cards, or it may be automatically assigned. For this case, it may be obtained from the report log file with a PRINT HFGROUP printout.

For this option, the TABDATA Cards of table T2 should contain a conductance multiplier. The dependent variable code on the TABTYPE Card of table T2 must be COND.

For more information on how the table data carried through to the SINDA file on file FMODLF, see the REFORM Module.

In addition to INTERP Cards, tables may also be referenced from Card 6e thermal couplings, user-written subroutines, PROP Physical Property Cards, and MAT Material Property Cards.