# TABLED1

Bulk Data Entry Defines a tabular function for use in generating frequency-dependent and time-dependent dynamic loads.

## Format

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
TABLED1 TID XAXIS YAXIS FLAT
x1 y1 x2 y2 x3 y3 x4 y4
x5 y5 etc. etc. etc. etc. etc. etc.

## Example

(1) (2) (3) (4) (5) (6) (7) (8) (9) (10)
TABLED1 32
-3.0 6.9 2.0 5.6 3.0 5.6 ENDT

## Definitions

Field Contents SI Unit Example
TID Table identification number.

No default (Integer > 0)

XAXIS Specifies a linear or logarithmic interpolation for the x-axis. 5
LINEAR (Default)
LOG

YAXIS Specifies a linear or logarithmic interpolation for the y-axis. 5, 6
LINEAR (Default)
LOG
SMOOTH

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.

Any x, y pair may be ignored by placing SKIP in either of the two fields used for that entry.

No default (Real or ENDT)

1. $xi$ must be in either ascending or descending order, but not both.
2. For example, in Figure 1 discontinuities are allowed only between points $x2$ through $x7$ . 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 $y=\left(y3+y4\right)/2$ .
3. At least one continuation entry must be specified.
4. The end of the table is indicated by the existence of ENDT in either of the two fields following the last entry. An error is detected if any continuations follow the entry containing the end-of-table flag ENDT.
5. 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 Linear $\frac{\mathrm{ln}\left({x}_{j}/x\right)}{\mathrm{ln}\left({x}_{j}/{x}_{i}\right)}{y}_{i}+\frac{\mathrm{ln}\left(x/{x}_{i}\right)}{\mathrm{ln}\left({x}_{j}/{x}_{i}\right)}{y}_{j}$
Linear Log $\mathrm{exp}\left[\frac{\left({x}_{j}-x\right)}{\left({x}_{j}-{x}_{i}\right)}\mathrm{ln}{y}_{i}+\frac{\left(x-{x}_{i}\right)}{\left({x}_{j}-{x}_{i}\right)}\mathrm{ln}{y}_{j}\right]$
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.

For FLAT=1, the same algorithm as FLAT=0 is used, except that values outside the range are not extrapolated. The corresponding start or end point y-values are used for all y-values outside the range.

6. SMOOTH option is only available for Explicit Dynamic Analysis (ANALYSIS=NLEXPL).
7. Linear extrapolation is not used for Fourier transform methods. The function is zero outside the range of the table.
8. For frequency-dependent loads, x# is measured in cycles per unit time.
9. Tabular values on an axis if X-Axis or Y-Axis=LOG must be positive. A fatal message will be issued if an axis has a tabular value ≤ 0.
10. This card is represented as a load collector in HyperMesh.