# TABLEG

Bulk Data Entry Defines a general tabular function for use in supported reference entries.

## Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
TABLEG TID LABEL TYPE XYTYPE FLAT
x1 y1
x2 y2
etc. etc.

## Example

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
TABLEG 32
-3.0 6.9
2.0 5.6

## Definitions

Field Contents SI Unit Example
TID Table identification number.

No default (Integer > 0)

LABEL Specify a name or label for the table.

Default = blank (<string> or blank)

TYPE Specifies a linear or logarithmic interpolation for the x-axis and y-axis. 4, 5
LINEAR (Default)
LOG
SMOOTH

XYTYPE Specifies how the X-axis and Y-axis are interpreted.
XY (Default)
First column is the X-axis and the second column is the Y-axis
YX
First column is the Y-axis and the second column is the X-axis

FLAT
Specifies the handling method for y-values outside the specified range of x-values in the table.
=0 (Default)
If an x-value input is outside the range of x-values specified on the table, the corresponding y-value look up is performed using linear extrapolation from the two start or two end points.
=FLAT or 1
If an x-value input is outside the range of x-values specified on the table, the corresponding y-value is equal to the start or end points, respectively.

x#, y# Tabular values.

No default (Real)

## Comments

1. $xi$ must be in either ascending or descending order, but not both.
2. Discontinuities may be specified between any two points except the two starting points or two end points. Also, if $y$ is evaluated at a discontinuity, the average value of $y$ is used. In Figure 1, the value of $y$ at $x=x3$ is $y$ = ( $y=\left(y3+y4\right)/2$ .
3. At least one continuation entry must be specified.
4. For FLAT=0 (default), TABLED1 uses the algorithm:(1)
$y={y}_{T}\left(x\right)$
Where,
$x$
Input to the table
$y$
Is returned
The table look-up is performed using interpolation within the table and linear extrapolation outside the table using the two starting or end points (Figure 1). The algorithms used for interpolation or extrapolation are:
X-Axis Y-Axis ${y}_{T}\left(x\right)$
Linear Linear $\frac{\left({x}_{j}-x\right)}{\left({x}_{j}-{x}_{i}\right)}{y}_{i}+\frac{\left(x-{x}_{i}\right)}{\left({x}_{j}-{x}_{i}\right)}{y}_{j}$
Log Log $\mathrm{exp}\left[\frac{\mathrm{ln}\left({x}_{j}/x\right)}{\mathrm{ln}\left({x}_{j}/{x}_{i}\right)}\mathrm{ln}{y}_{i}+\frac{\mathrm{ln}\left(x/{x}_{i}\right)}{\mathrm{ln}\left({x}_{j}/{x}_{i}\right)}\mathrm{ln}{y}_{j}\right]$
Linear Smooth ${y}_{i}+\left({y}_{j}-{y}_{i}\right)\frac{{\left(x-{x}_{i}\right)}^{3}}{{\left({x}_{j}-{x}_{i}\right)}^{3}}\left(10-15\frac{\left(x-{x}_{i}\right)}{\left({x}_{j}-{x}_{i}\right)}+6\frac{{\left(x-{x}_{i}\right)}^{2}}{{\left({x}_{j}-{x}_{i}\right)}^{2}}\right)$

Where, ${x}_{j}$ and ${y}_{j}$ follow ${x}_{i}$ and ${y}_{i}$ .

No warning messages are issued if table data is input incorrectly.
5. SMOOTH option is only available for Explicit Dynamic Analysis (ANALYSIS=NLEXPL).
6. Linear extrapolation is not used for Fourier transform methods. The function is zero outside the range of the table.
7. For frequency-dependent loads, x# is measured in cycles per unit time.
8. Tabular values on an axis if TYPE =LOG must be positive. A fatal message will be issued if an axis has a tabular value ≤ 0.
9. TABLEG can be used in the following situations:
• TABLEG can be used instead of TABLED1, on the RLOAD and TLOAD Bulk Data Entries.
• TABLEG can be used instead of TABLEM1, on the MATT# entries.
• TABLEG can be used instead of TABLES1, on the MATS1, MCIRON or PCONT entries.
10. TABLEG identification numbers should be unique with regard to any other TABLE# entry. TABLEG should not have the same ID as any other TABLE# entry.
11. If there are any unused TABLEG entries in the input file, there will not be any warning in the .out file.