# .#.slk file

The .slk file is a Microsoft Excel SYLK Format results file.

## File Creation

This file is only created when size or shape optimization is performed. Output of this file is controlled by the SENSITIVITY and SENSOUT I/O Options.

## File Contents

The file contains sensitivity information for size and shape design variables.

## File Format

The only values that can be changed in this file are those listed in the "New" column. All other values are either fixed or their calculation is fixed. When the .slk file is created, the values in the "New" column match those in the "Reference" column. These values may be adjusted, but should always remain within the design variable's bounds.

Each size and shape design variable in the model is listed in the left-hand column of the sensitivity table. Information concerning a particular design variable is given in the row where its label is listed. The current value and the upper and lower bounds of the design variables are given in the columns, "Reference," "Lower," and "Upper", respectively.

Each referenced response in the model has its own column. These response columns are on the right-hand side of the sensitivity table. The calculated sensitivity of a response to changes in a design variable at the current iteration is given in the row corresponding to that design variable and the column corresponding to that response.

Beneath the list of design variables, in the left-hand column, are the headings "Response lower bound," "Response reference," and "Response upper bound". If a response is constrained, the constraint value will be given in either the "Response lower bound" or the "Response upper bound" row of the column corresponding to that response. The value given in the "Response reference" row is the calculated value of the response using the design variable reference values.

At the bottom of the left-hand column are the headings: "Response linear," "Response reciprocal," and "Response conservative". The response values in these rows are the predicted values of the responses for three different approximations. Initially, these values will match one another and the "Response reference" value for each response. This is because these are the predicted values of the response at the given variable settings, which initially are the same settings used to calculate the "Response reference" value. Once the design variable values in the "New" column are altered, these values will change.

The "Response linear" row predicts the response value using linear approximation. This is calculated as:(1)
${R}_{1}={R}_{0}+\frac{dR}{dv1}\left(v1-v{1}_{0}\right)+\frac{dR}{dv2}\left(v2-v{2}_{0}\right)+\dots +\frac{dR}{dvn}\left(vn-v{n}_{0}\right)$
Where,
R1
Predicted response value.
R0
Response reference value.
v1, v2, . . . ,vn
The new values of the design variables.
v10, v20, . . . ,vn0
The reference values of the design variables.
$\frac{dR}{dv1},\frac{dR}{dv2},\cdots \frac{dR}{dvn}$
The sensitivities of the response to the design variables.
The "Response reciprocal" row predicts the response value using reciprocal approximation. This is calculated as:(2)
${R}_{1}={R}_{0}-\frac{dR}{dv1}v{1}_{0}^{2}\left(\frac{1}{v1}-\frac{1}{v{1}_{0}}\right)-\frac{dR}{dv2}v{2}_{0}^{2}\left(\frac{1}{v2}-\frac{1}{v{2}_{0}}\right)-\dots -\frac{dR}{dvn}v{n}_{0}^{2}\left(\frac{1}{vn}-\frac{1}{v{n}_{0}}\right)$
Where,
R1
Predicted response value.
R0
Response reference value.
v1, v2, . . . ,vn
The new values of the design variables.
v10, v20, . . . ,vn0
The reference values of the design variables.
$\frac{dR}{dv1},\frac{dR}{dv2},\cdots \frac{dR}{dvn}$
The sensitivities of the response to the design variables.

The "Response conservative" row predicts the response value using a combination of the above approximations where linear approximation is used, when the sensitivity is positive, and reciprocal approximation is used when the sensitivity is negative. Therefore, if all sensitivities are positive, the conservative prediction will match the linear prediction. If all sensitivities are negative, it will match the reciprocal prediction, but if there is a mixture of positive and negative sensitivities for a given response then the conservative prediction will match neither the linear nor the reciprocal prediction.

The normalized values simply show the predicted response as a fraction of the response reference value.