Initial Values of Density (DENSITY_INITIAL)

The relative density of each element is the design variable in topology optimization. In the initial optimization iteration, the design space has a homogenous material distribution, meaning that each element contains the same relative material volume.

See Also
In Other Guides
OPT_PARAM

Initially, all the elements get the density causing the material volume constraint to be exactly fulfilled if a material volume constraint is defined for the optimization problem.

When no volume constraint is present in the optimization problem but the relative material volume is used in the objective function, each element has an initial relative density of 50%. However, if the constraints (for example, displacement constraints) require a significantly higher relative material volume than 50% for being fulfilled and this is known before the optimization, then the initial relative material volume in the design space can be set to a larger value (for example, to 90%) using the command DENSITY_INITIAL:

OPT_PARAM
 ID_NAME         = opt_params
 OPTIMIZE        = id_of_optimize
 DENSITY_INITIAL = 0.9
END_

Similarly, if it is known before the optimization that the relative material volume of significantly less than 50% is required in order to fulfill the constraints, the initial relative material volume can be set to a lower value (for example, to 10%):

OPT_PARAM
 ID_NAME         = opt_params
 OPTIMIZE        = id_of_optimize
 DENSITY_INITIAL = 0.1
END_

In both cases, it will lead to lower number of optimization iterations.

Important:
  • The default value of DENSITY_INITIAL is 0.5. DENSITY_INITIAL should always be greater than zero and lower than or equal to one.
  • The DENSITY_INITIAL parameter can be used to stabilize nonlinear or contact problems in combination with volume constraints. Setting a higher material volume in iteration 0 leads to an initially infeasible volume constraint requiring more optimization iterations. Nevertheless the higher initial stiffness improves the convergence behavior of the finite element solver in the first optimization iterations.
  • Relative values in constraints always refer to the design response of the start model for the optimization. In topology optimization, this start model is the model with eventually adapted element densities, which may differ from the initial model (for example, when no volume constraint is present they are set to 50% of the original density). Take this into account when defining, for example, relative displacement or frequency constraints. This behavior can be controlled by the user with the parameter DENSITY_INITIAL in the OPT_PARAM command.