There are three different plate expansion methods which you can choose from. In most cases the General method should be used, however, there may be times when either of the other two methods may be more suitable. Details of the different methods are given below:

The General method is the most versatile and is designed to work with plates which have either positive, negative or zero Gaussian curvature. A greater degree of control over the development is available with this algorithm allowing you to match the development to your plate forming machinery.

Positive Gaussian curvature occurs in plates with double curvature in the same direction, either inwards or outwards so that the plate is purely convex or concave. Negative Gaussian curvature occurs in plates which are twisted or saddle shaped. Zero Gaussian curvature plates a developable and can be developed with requiring any stretching or shrinking.

The General Method - Forming Direction, General Method - Strain Ratio and General Method - Forming Process items in this dialog will only be available if the General method is selected.

This option is used to specify the direction in which the plate is to be rolled; this is the direction in which the maximum strain will be put into the plate.

The Ideal option will try to form the plate in the direction of minimum principal curvature. This is calculated as weighted average over the whole plate. Theoretically, forming in this direction will require the minimum amount of plate stretching or shrinking. Due to constraints of plate forming machinery or other production reasons, you may wish to expand in a different direction.

To give you this control, Workshop allows you to specify either the plate's longest axis or its shortest axis directions. (These directions are local to the plate and do not necessarily correspond to the global ship axes.) Note that if you select Ideal, the forming direction will snap to the plate's longest or shortest axis if the direction of minimum principal curvature is within 10 degrees of these directions.

The forming directions “Ship longitudinal axis” and Ship transverse axis” are useful for mirrored plates when you wish the expansion direction to be parallel or normal to the mirrored edge; otherwise the expansion direction will also be mirrored for the two halves of the plate.

Note that the forming direction will only affect the result if the strain ratio (see below) is less than 100%. Also note that if the plate is being formed by line heating, the maximum shrinkage will be perpendicular to the heating lines. The forming direction, described above, refers to the direction in which the maximum strain magnitude will occur; thus this will be perpendicular to the direction of line heating but parallel to the plate rolling lines.

The forming direction used is indicated by an arrow which is displayed along with the plate in the Part view.

The strain ratio relates the strain in the direction perpendicular to the direction of maximum strain to the maximum strain. If the strain ratio is 100% then the strain does not depend on the orientation, it is isotropic. If the strain ratio is 0%, the expansion is purely uni-directional and there will be no strain in the direction perpendicular to the direction of maximum strain. Forming methods such as peening and planishing produce isotropic strain distributions, whereas line heating and rolling produce a more uni-directional strain distribution.

The figures below show the effect of strain ratio and forming direction on the expansion of a plate with negative Gaussian curvature. For this plate the forming direction was set to longitudinal with 0% strain ratio. As one would expect, the results show positive longitudinal strain on the edges, with the transverse strain remaining virtually zero. In the figures below, red areas show high positive strain and green areas have zero strain.

Longitudinal strain for negative Gaussian curvature plate: Expand only with 0% Strain Ratio.

Transverse strain for negative Gaussian curvature plate: Expand only with 0% Strain Ratio.

You may choose whether you wish to preserve the plate edge lengths, stretch the plate (expand only) or shrink the plate. Most processing methods will expand the plate, however line heating will shrink the plate.

Using the Preserve Lengths method will ensure that the expanded plate edges are always the same length as the 3D surface plate. This may result in positive, negative or a mixture of positive and negative strain in the interior of the plate.

If you choose the Expand or Shrink options, the strain in the plate will be uniformly increased or decreased so that the overall strain is either all positive or all negative, depending on the selection made. (Note that there are small in built tolerances on the strain values.)

For plates with positive Gaussian curvature, selecting Expand only, will result in a plate where the middle requires stretching whilst the perimeter will remain unchanged. For a similar plate, choosing Shrink only, will result in the middle of the plate being unchanged whilst the edges will need to be shrunk (In the figures below, green areas have no strain; red areas positive strain and blue areas negative strain:

Positive Gaussian Curvature Plate: Expand Only; centre of plate requires stretching, edges remain unchanged.

Positive Gaussian Curvature Plate: Shrink Only; centre of plate remains unchanged, edges require shrinking.

Negative Gaussian Curvature Plate: Expand Only; centre of plate remains unchanged, edges require stretching.

Negative Gaussian Curvature Plate: Shrink Only; centre of plate requires shrinking, edges remain unchanged.

Whilst the General method is robust, it may have problems with surfaces which have a very large variation in local surface normal, e.g. a complete hemisphere. If such problems are encountered, the plate should be subdivided further.

The computations required for the General method can be quite intensive. It is advisable to check the results at lowest or low precision before completing the calculations at medium precision. For the General method, high and highest precision use the same plate mesh as medium precision. See: Plate Precision on page 65

This method may be useful for plates which have zero or slightly negative Gaussian Curvature. It has the advantage of being quicker to compute than the General method.

This method should be used if you are using workshop to develop fabric panels. The method models the way in which a fabric stretches most along its bias direction. With this method angles will tend to distort whilst the lengths remain constant; with the other methods, angles will tend to remain constant whilst the lengths change.

Workshop allows you to specify the number of line segments that is used to draw the expanded plate. For very long and skinny plates you may wish to use the Manual plate precision setting on the bottom of the Plate Info dialog. Decreasing the number of line segments on the short edge, can reduce computation time while not compromising the accuracy.

The automatic precision uses the Workshop Precision as it is set in the program’s Data menu. In general it is recommended to use the Automatic setting for the plate precision.