Run 2D topology optimization using the SIMP (density) method in real time in your browser. Change loads, boundary conditions, and volume fraction to intuitively explore optimal material distribution.
Parameters
Boundary Condition Presets
Volume constraint V* [%]
%
Fraction of material allowed. Lower values yield lighter but more complex structures.
Mesh resolution
Load direction
Iteration0 / 50
Compliance—
Volume fraction—
Change Δρ—
SIMP method overview
Assign density ρ∈[0,1] to each element.
Set stiffness as E = Emin + ρp·E₀ (p=3).
Updating densities via OC method while satisfying volume constraint
Minimize compliance (flexibility).
Results
Compliance
—
Normalized value
Volume fraction
—
%
Mesh
40×20
elements
Solid elements
—
count
Density Distribution (Topology Optimization Result)
CantileverIter: 0
Solid (ρ≈1)
Intermediate density
Void (ρ≈0)
Compliance Convergence
What is SIMP topology optimization?
🙋
What does topology optimization do? Is it just a lightweighting trick?
🎓
It is more than removing material. The optimizer decides where material should remain so the structure carries the applied loads efficiently under a volume constraint. Change the boundary-condition preset, run the solver, and watch how the load path becomes a frame-like pattern.
🙋
Why do gray intermediate-density regions appear during the calculation?
🎓
SIMP treats each element as a density between void and solid. The penalty exponent makes intermediate density inefficient, so the final design tends toward a clear 0-or-1 layout. The filter radius also suppresses checkerboard artifacts.
🙋
Can I manufacture the shape exactly as shown?
🎓
Treat it as a design concept. In real projects, engineers rebuild the result into manufacturable ribs, fillets, wall thicknesses, and connection features before detailed finite-element validation.
Frequently Asked Questions
The penalty factor may be too low, the volume constraint may be too loose, or the filter radius may be too large. Stronger penalization and a tighter volume target make the design more binary.
They define the load path the optimizer tries to preserve. A small change in support location or force direction can completely change the optimal topology, so always verify that the boundary conditions match the intended design case.
The result is best used as a layout guide. Convert it into clean CAD geometry, add manufacturing constraints, and then re-check stresses, buckling, fatigue, and connection details.
Real-World Applications
Aerospace brackets: Topology optimization helps identify stiff load paths while reducing mass in engine mounts, seat supports, and payload brackets.
Automotive structures: Suspension arms, mounts, and crash-relevant reinforcements can be redesigned to reduce weight while preserving stiffness.
Additive manufacturing: Organic rib networks suggested by topology optimization often become starting points for 3D-printed metal parts.
Common Misconceptions and Notes
The optimizer does not produce a final drawing by itself. Very thin members, sharp corners, and disconnected islands must be interpreted carefully. Start with moderate mesh resolution and a 40-60% volume fraction to understand the trend before pushing the design aggressively.