Goals and Constraints

In the Goals and Constraints PropertyManager, you specify the optimization goal and the constraints that drive the mathematical formulation of the optimization algorithm.

To access the Goals and Constraints PropertyManager:

  • In a Topology study tree, right-click Goals and Constraints, and select one of the three optimization goals: Best Stiffness to Weight Ratio, Minimize Mass, or Minimize Maximum Displacement.

Select Goal

  Best Stiffness to Weight ratio (default) The optimization algorithm yields the shape of a component with the largest stiffness considering the given amount of mass that will be removed from the initial maximum design space.

When you select Best Stiffness to Weight ratio, the algorithm seeks to minimize the global compliance of the model, which is a measure of the overall flexibility (reciprocal of stiffness). Compliance is defined by the sum of strain energies of all elements.

  Minimize Maximum Displacement The optimization algorithm yields a shape that minimizes the maximum displacement on a single node (calculated from a static study). With a given percentage of material to remove from a component, optimization yields the stiffest design that weighs less than the initial design and minimizes the maximum observed displacement.
  Minimize Mass with Displacement Constraint

The optimization algorithm yields a shape that weighs less than the maximum size model and does not violate the given target for the displacement constraint. The algorithm seeks to reduce the mass of a component while restricting the displacement (max observed value of component or user-defined at a single node) under a certain limit.


Constraints limit the design space solutions by enforcing limits on the amount of mass that can be reduced and performance targets for the optimized model. The User Interface filters the type of constraints you can apply based on the optimization goal you select. You can specify mass, displacement, frequency, or stress constraints.
  Mass constraint Specify the targeted mass that the part will be reduced by during optimization. Select one of the following:

Reduce mass by (percentage)

Type the targeted percentage of mass reduction.

Reduce mass by (absolute value)

Type the exact value of the mass to remove from the part's maximum design space.

The optimization algorithm will attempt to reach the targeted mass reduction for the final shape through an iterative process.
  Displacement constraint Specifies the upper limit for the selected displacement component. In Component, select the required displacement variable. Select one of the following:

Specified value

Type the targeted value for the selected displacement variable, and specify the required units in Units.

Specified factor

Type a factor to multiply the maximum displacement calculated from a static study.

Select one of the following for a reference vertex location for the displacement constraint:

Automatic (single max point)

The program selects by default the vertex of the maximum displacement observed in the model.

User defined

Select in the graphics area the reference vertex for the displacement constraint.

  Frequency Constraint

Mode Shapes

Add the number of mode shapes to enforce a frequency constraint during optimization.

Before you run a topology study, run a frequency study with the original model (maximum design space) to evaluate the range of permissible natural frequencies.


Select one of the three options: is less than to enter an upper frequency limit, is greater than to enter a lower frequency limit, or is between to enter a range of permissible frequencies for the selected mode shape (for example, 10-20).

Value (Hz)

Enter the frequency values in Hz for each mode shape.

Mode tracking

When selected, the optimization solver tracks the order of the selected mode shapes as derived from the original geometry when enforcing frequency constraints throughout the optimization iterations. When Mode tracking is cleared, the solver tracks the current order of mode shapes as derived for each optimization iteration. For example, it is possible for an optimization goal of a 50% mass reduction and a frequency constraint on the first mode shape, the first mode shape of the original geometry becomes the second or third mode shape of the optimized geometry.

For example, you add a frequency constraint on a distinct bending mode shape of a plate (the first mode in the original plate geometry). As the model shape changes during iterations, this distinct bending mode may move down in the frequency list. By selecting Mode tracking, the solver keeps track of the same mode as it moves positions in the list of frequencies, and enforces the constraint on the same mode shape. When you clear Mode tracking, another mode shape may replace the original first bending mode in the course of iterations. The solver then applies the frequency constraint on this new mode that replaces the old mode.
  Stress/Factor of Safety Constraint

Stress Constraint

Select Specified value to enter the maximum permissible von Mises stress for the optimized geometry. Select Specified percentage to enter the maximum permissible von Mises stress as a percentage of the material's yield strength.

Factor of Safety Constraint

Enter a minimum factor of safety value for the optimized geometry. The default failure criterion is the Maximum von Mises stress.

For a Topology study with specified frequency constraints only:

  • Applied loads or prescribed displacements (including remote loads, translations, and rotations) are not considered in the calculation of the resonant frequencies.
  • To apply a remote mass, in the Remote Load/Mass PropertyManager, select Connection Type > Rigid. Any remote mass you apply with option Connection Type > Distributed is ignored by the solver.