Shape Panel

If you select move limit =, you must specify a limit value.

If you choose ddvale =, click the button to select an existing ddvals.

In the case of non-linear design variables, how the variable is applied (via the by constraint / by system / by mid-shape switch that displays for nonlinear desvars.)

by constraint

Assumes that constraints, such as those which force nodes to move along or are bounded by a line, plane, surface, mesh, or equation, make the shape non-linear. When you click create Engineering Solutions applies each selected shape a number times between the lower and upper bounds, applying the constraints each time. From these applications, the non-linear path for each node will be calculated for each shape and up to four new shapes and design variables (per shape) will be generated which, through equations which link them together, will describe the non-linear motion of the shapes as they are affected by the constraints. For bounded style constraints, where nodes are allowed to move up to but not past a feature such as a surface, you should create any shape which is affected by such constraints with the limiting constraints made inactive. In other words, the nodes should pass through the constraint when the shape is applied. Then, before creating the non-linear shapes, make the limiting constraints active again. This will ensure that the path of the nodes will be non-linear, moving up to the constraint and then stopping, rather than linearly moving up to the constrained position. You can set which constraints are active and inactive in the HyperMorph panel > Morph Options panel. Due to the limitations of simulating bounded constraints via equations, the constrained nodes may stop slightly short or pass slightly beyond the constraints for some values of application during optimization.

Figure 1. Two Meshes Constrained to a Cylindrical Surface. The mesh on the left slides along the surface, while the mesh on the right is bounded by the surface. Both shapes need to be converted into nonlinear design variables to perform during optimization as they do during morphing. The shape on the right will move the mesh through the surface if the bounding constraint is inactive. This is how shapes to be converted to nonlinear shapes should be defined when bounding constraints are used. The bounding constraint must be made active when creating non-linear design variables.

by system

Intended for shapes which were created by rotating the mesh using the angle or arc angle options in the HyperMorph panel > Alter Dimensions panel > Shapes panel which were created with respect to a cylindrical coordinate system, or any shapes whose nodes are intended to move in the r-theta-z directions rather than the x-y-z directions. To use this option you must select a local coordinate system about which the selected shapes rotate. Engineering Solutions will then determine the non-linear paths of the nodes for each shape as they travel around the local coordinate system and create up to four new shapes for each shape which, through equations which link them together, describe the non-linear paths of the nodes.

Figure 2. Two Shapes Created with Respect to a Cylindrical Coordinate System. n the top figure, the arc angle of the mesh is changed and in the bottom figure, the radius of the mesh is changed. Both shapes act with respect to the cylindrical coordinate system, the first by moving nodes in the theta direction and the second by moving nodes in the radial direction. These shapes should be converted to non-linear design variables using the by system option so that the mesh maintains its true curvature during optimization.

by mid-shape

Create a non-linear shape described by two shapes. One shape represents the non-linear shape when it is applied with a multiplier of one. The other shape represents the non-linear shape when it is applied with a multiplier of one-half. HyperMorph will interpolate the non-linear paths of the nodes as they travel from the undeformed position to the mid-shape position to the full shape position. HyperMorph will then create three shapes which, through equations which link them together, describe the non-linear paths of the nodes.

Figure 3. Non-Linear Path. The non-linear path (yellow) for a node is calculated as starting at the undeformed position, passing through the half-shape position (blue), and finishing at the full-shape position (magenta).

Figure 4. Arc Angle Shape Change Applied Simultaneously with a Radius Shape Change. In the left figure the two shapes are applied with no compensation. Notice how the sides of the mesh no longer line up with the axis of the local coordinate system. In the right figure the compensation shape has been applied. Notice how the sides of the mesh now line up with the center axis of the local coordinate system. If both shapes are converted into non-linear design variables at the same time, the compensation design variable will be generated and integrated into the optimization automatically.

When applied during optimization, the non-linear shapes will be close to, but probably not exactly aligned with, the intended node paths. Although the generated shapes and equations have been optimized to minimize the amount of error between the intended node paths and the actual node paths it is not possible to precisely mimic every non-linear shape using a combination of linear ones. However, this feature should allow sufficient fidelity for most optimization applications.

Shapes to be converted into non-linear shapes perform best when they have either a lower bound or upper bound of 0.0, but good fidelity can be achieved for shapes which have a negative lower bound and positive upper bound. However, non-linear shapes which sweep out an arc of more than 90 degrees may not give good fidelity for intermediate values.