Density Model
The Density Model feature () can be added from the model tree under Component>Definitions using the Topology Optimization context menu. It includes settings for
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Filtering
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Projection
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Interpolation
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Discretization
Variables
The Density Model feature adds
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A domain control variable field (dtopo#.theta_c) (control material volume factor)
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A domain dependent variable (dtopo#.theta_f) (filtered material volume factor)
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A domain variable (dtopo#.theta) (projected material volume factor)
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A domain variable (dtopo#.theta_p) (penalized material volume factor)
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A global variable (dtopo#.theta_avg) (average material volume factor)
The control variable field is bounded to the interval [0;1]. It is used as input to a Helmholtz filter, which introduces a minimum length scale. The projected material volume factor is fixed to 1 outside the selection for the Density Model feature.
For a more extensive introduction to the mathematics implemented by this feature, see Theory for Topology Optimization.
Filtering
From the Filter type list, choose between no filtering (None) and a Helmholtz filter (Helmholtz; the default), which can impose a minimum length scale by means of a filter radius Rmin (SI unit: m). The local mesh element size h is the default value because this radius should not be smaller than the mesh element size. However, a fixed length scale must be used to get mesh-independent results.
Projection
From the Projection type list, specify no projection (None; the default) or projection based on the hyperbolic tangent function (Hyperbolic tangent projection). When using projection, you can choose the projection point and the projection slope. Projection with a large slope produces designs almost free of intermediate values, but the optimization problem will be difficult to solve if the slope is too large.
Interpolation
The feature supports, using the Interpolation type list, RAMP and SIMP interpolation for solid mechanics, while Darcy interpolation can be used for fluid mechanics. You can also choose a Linear or a User defined interpolation. For solid mechanics it is common to interpolate the Young’s modulus, and the relative void stiffness can be bounded using the minimum penalized volume fraction, θmin. The SIMP exponent pSIMP and the RAMP parameter qRAMP properties determine the stiffness for intermediate design variables. Values in the interval [2;4] produce well-defined topologies in the context of volume-constrained compliance minimization. For fluid mechanics it is common to introduce a volume damping force, which should be large in the solid regions. The maximum value, however, depends on the fluid viscosity as well as the mesh size, so it is up to you as the user to specify this value. The Darcy penalization parameter controls the damping for intermediate design variables, and a value of 1 works well in the context of volume constrained dissipation maximization, but sometimes a continuation starting from a lower value is required to find the global minimum.
Note that you can use the dtopo#.theta_avg variable to impose a volume constraint and the dtopo#.theta variable to write a custom material interpolation.
Discretization
The  Linear discretization gives a continuous representation by associating the design variables with the mesh nodes, while an elementwise Constant discretization gives a discontinuous representation, which generally gives rise to more variables than the Linear discretization.
The Initial value θ0 should be set such that the starting design does not violate any optimization constraints.