Topology Optimisation for AM: Beyond the Organic Shape

Topology optimisation (TO) generates parts that look like they were designed by nature: branching load paths, organic transitions, material distributed exactly where stresses demand it. Additive manufacturing can build shapes that conventional machining cannot. The combination seems obvious.

But the organic geometry that falls out of a topology optimiser is almost never directly printable. It contains near-horizontal overhangs, sub-millimetre features, sharp re-entrant corners, and void regions that are impossible to depowder. Between the TO result and a printable file sits a non-trivial engineering workflow.

This article explains what topology optimisers actually compute, why the AM-TO combination requires specific constraints, and the practical steps from load case definition to a part that will survive the build.

What topology optimisation actually computes

Topology optimisation is a material distribution method: it decides which regions of a design space should contain material and which should be empty. The dominant formulation used in commercial software is the SIMP method (Solid Isotropic Material with Penalisation), developed by Bendsøe and Sigmund in the 1990s.

In SIMP, every finite element in the design domain is assigned a density variable ρ ranging from 0 (void) to 1 (solid). The element stiffness is penalised as ρ^p (typically p = 3), which drives intermediate densities toward 0 or 1 — creating a binary solid/void result.

The standard optimisation problem is:

Minimise: structural compliance C = f^T u (the inverse of global stiffness — minimising compliance maximises stiffness)

Subject to: V/V₀ ≤ f (volume fraction constraint — keep total material below a specified fraction)

And: 0 ≤ ρ ≤ 1 for all elements

The result is the stiffest possible structure that uses no more than a specified fraction (typically 20–50%) of the original design volume, for the applied load cases.

This formulation has clear limits. It assumes linear elasticity and a single dominant load case (or a weighted combination). It does not inherently consider buckling, fatigue, dynamic loads, or manufacturing constraints — unless these are explicitly added. Understanding what the optimiser is actually doing prevents the common mistake of treating its output as a final design.

Why AM unlocks topology optimisation

Before metal AM, TO was largely academic. A topology-optimised titanium bracket might save 40% mass — but machining the result from a billet was impossible and casting the organic geometry was impractical. The part stayed on paper.

Metal LPBF changed this. The process builds material layer by layer, unconstrained by tool paths or parting lines. Organic lattice-like structures, internal voids, smoothly varying cross-sections — all of these are buildable. For the first time, the theoretical output of a topology optimiser could be turned into physical hardware at reasonable cost.

The practical evidence of this is extensive. Published cases from aerospace programs show:

• Airbus A320 nacelle hinge bracket: 30% mass reduction after TO + LPBF redesign (Airbus / APWorks, 2014)
• GE aviation fuel nozzle: 25% lighter, 5× life improvement (GE, 2015) — though this used lattice infill + TO together
• Medical tibial implants: 20–35% mass reduction vs. solid implant designs while matching bone stiffness

The combination works. But the path from TO output to these printed parts was not trivial.

The AM-specific topology optimisation problem

Standard TO formulations — as implemented in most FEA packages — have no concept of the build direction, the self-supporting angle constraint, the minimum printable feature size, or the powder removal requirement. The output is purely mechanical-stiffness-optimal.

This creates predictable AM-printability failures in naive TO outputs:

Near-horizontal members: A standard SIMP result almost always contains horizontal or low-angle members connecting vertical load paths. These require dense support structures — which add cost, potentially exceed material volume savings, and may be irremovable if they are inside a lattice cavity.

Sub-millimetre features: SIMP distributes material in mathematically thin connections. For LPBF with a 30–50 µm melt pool, the minimum reliable strut diameter is 0.3–0.5 mm, and the minimum wall is 0.3–0.4 mm. TO outputs routinely contain connections below this scale.

Enclosed voids: TO may create fully enclosed internal voids if the load case rewards it. In powder bed fusion, enclosed voids trap powder permanently — a reject condition for most applications.

Staircase surfaces: The voxel-based TO result, after isosurface extraction, has a staircase quality from the FEA mesh. This is not a visual problem — the facets introduce stress concentrations and printability artefacts if not smoothed.

AM-aware topology optimisation constraints

The response to these problems is to build manufacturing constraints directly into the TO problem. This is now an active research and software development area, and commercial tools have begun implementing some of these constraints.

Overhang (build-direction) constraint

The build-direction constraint penalises the formation of horizontal or low-angle material interfaces in the build direction. The implementation varies by software, but the conceptual approach is to add a term to the optimisation objective that penalises any material that is not supported by material in the layer below (within the self-supporting angle threshold).

Lazarov et al. (2016) and Wang et al. (2017) published early formal implementations. The result is a TO output that inherently avoids significant overhangs — at the cost of slightly higher compliance than the unconstrained solution (typically 5–15% stiffer for the same volume fraction is sacrificed).

In practice, the overhang constraint must be applied with a specified build direction. If you do not know the build direction at TO time, you either run multiple TO solutions for candidate orientations or use a build-direction-agnostic penalty that approximately self-supports in all directions (resulting in tree-like, root-growing-downward geometries).

Minimum length scale (filter radius)

The SIMP method naturally produces intermediate densities that the penalisation scheme drives to 0 or 1. But without a minimum length scale control, the result has features that scale with the mesh element size — which can be arbitrarily small.

Length scale control is implemented via a density filter: a spatial averaging of element densities over a radius r before penalisation. This enforces that no feature can be smaller than approximately 2r. For LPBF printability, the filter radius should be set to give a minimum feature size of at least 0.5 mm (≈ 2× the typical melt pool width of 0.2–0.25 mm).

In most TO software, this is set by the "minimum member size" or "filter radius" parameter.

Layer-by-layer (layerwise) density check

An extension of the overhang constraint checks not just that individual elements are supported, but that the density distribution can be built layer by layer — i.e., each cross-section at height z has sufficient material connection to the section at z − Δz. This prevents disconnected islands of material that would not be buildable even if each individual surface is technically above the self-supporting angle.

Software landscape

Commercial TO tools with AM awareness

Altair OptiStruct: The most mature commercial structural optimiser. As of recent versions, includes overhang constraints and minimum member size controls. Widely used in aerospace structural programs. Integrates with HyperMesh and HyperView for pre/post-processing. Strong in fatigue and dynamic load cases.

Autodesk Fusion Generative Design: Cloud-based generative design (effectively TO + manufacturing constraint library). Supports LPBF, machining, and casting constraints simultaneously. Generates multiple variants for different manufacturing methods and lets the user compare. More accessible interface than traditional FEA-based tools but less control over the optimisation formulation.

nTop Platform (nTopology): Not a pure TO tool, but a geometry kernel that can ingest TO results and apply DfAM post-processing programmatically — smooth, thicken, lattice infill, export. Strong for the geometry processing steps after TO rather than the optimisation itself.

Ansys OptiStruct (via Ansys Mechanical): Ansys' implementation of TO, competitive with Altair for structural FEA workflows. Includes overhang and manufacturing constraint options in recent versions. Note: "Ansys Optistrucct" in Ansys branding refers to the same capability.

Siemens NX Topology Optimisation: Integrated in the NX CAD/CAE environment. Better for users already working in the NX ecosystem (common in aerospace and automotive).

Open-source options

99-line MATLAB code (Sigmund, 2001): The foundational teaching implementation of SIMP. Widely reproduced and extended. Not a production tool but the fastest way to understand what TO actually computes. Available freely.

OpenTOPOPT / top88 / top3d: Open-source MATLAB and Python SIMP implementations for research and education. No AM constraints out of the box but extensible.

BESO scripts (RMIT group): Bi-directional Evolutionary Structural Optimisation — an alternative to SIMP. Open implementations available in MATLAB. Can produce different geometry characteristics from SIMP (more rounded, less spindly structures in some configurations).

FEniCS / OpenFOAM-based TO: Academic implementations using open-source FEA frameworks. High computation cost, steep learning curve, but maximum flexibility for custom constraints.

Smooth to printable: the workflow

Raw TO output is not a printable file. The workflow from TO result to submitted part file has six recognisable steps.

Step 1 — Run TO with appropriate constraints. Define the design domain, non-design regions (keep-out zones for fixings, mating faces), load cases, volume fraction target, build direction, and minimum member size. Run the optimisation.

Step 2 — Isosurface extraction (marching cubes). The TO result is a density field on a voxel grid. To get a surface mesh, apply an isosurface algorithm (marching cubes is standard) at a density threshold — typically ρ = 0.3–0.5. The choice of threshold changes the total material volume; tune it to match the volume fraction target.

The output is an STL or surface mesh — typically faceted and rough.

Step 3 — Laplacian smoothing. Apply 5–20 iterations of Laplacian smoothing to the surface mesh to remove the staircase artefacts. This slightly rounds all edges and reduces sharp features. In nTop, Meshlab, or 3-matic, this is a one-click operation. Verify that smoothing has not moved functional surfaces (holes, interfaces) out of tolerance — smooth with control vertices locked on these regions.

Step 4 — DfAM check. Re-run the smoothed mesh through a DfAM analysis:

• Check all surfaces against the self-supporting angle threshold — did the overhang constraint work, or are there remnant low-angle faces?
• Verify minimum wall and strut thickness (measure thin sections)
• Check for enclosed voids — add drain/vent holes if needed
• Confirm that the support interfaces are accessible

The DfAM checklist tool provides a structured walkthrough.

Step 5 — Optional lattice infill. If the TO result has thick solid regions (common in bending-dominated structures), these regions can be replaced with a structural lattice — typically a gyroid, octet truss, or body-centred cubic cell. This reduces mass further, beyond what TO achieves with solid material, at the cost of more complex support removal and potential trapped powder risk. Lattice design should be reserved for regions where the local stress state is relatively uniform (confirmed by stress analysis, not assumed).

Step 6 — Structural validation. The final smoothed, DfAM-compliant geometry is not mechanically identical to the TO result that was analysed. Smoothing, threshold changes, and added features all modify the stiffness and stress distribution. Always run a final FEA on the as-designed geometry to confirm it meets the structural requirement. For fracture-critical applications, a fatigue analysis is needed — the TO result optimises static compliance, not fatigue life.

When TO makes sense vs. when it does not

Topology optimisation is high-value when:

Load-critical metallic parts with clear load cases and mass is a premium. Aerospace brackets, satellite structures, aircraft seat fittings, race car uprights. The combination of clear structural loading, expensive material (titanium, Inconel), and mass-sensitive applications creates the conditions where 30–50% mass savings justify the engineering investment.

Complex load transfer nodes. Multi-axis brackets, fittings that must transfer loads in three dimensions without a clean prismatic solution. TO finds non-obvious material distributions in these cases.

Heat exchangers and thermal structures. Some TO formulations optimise thermal conductance rather than mechanical stiffness. For AM heat exchangers with complex channel geometry, TO can find optimal fin distributions.

Topology optimisation adds limited value when:

The geometry is already well-optimised by conventional design rules. A simple prismatic bracket with a dominant axial load has very little material to remove — the conventional beam or plate design is already near-optimal. TO will give you an organic shape that is marginally lighter but much more expensive to post-process and inspect.

You do not have well-defined load cases. TO is only as good as its inputs. Poorly defined or incomplete load cases produce results optimised for the wrong conditions — which may fail in service at load combinations not included in the optimisation.

The feature is too small for the minimum printable scale. TO becomes irrelevant if the part is already near the minimum wall thickness or strut diameter limit — there is nothing to remove without compromising printability.

Post-processing drives cost more than material. For materials like gold or platinum (AM jewellery), raw material cost dominates. For these, mass reduction from TO does translate to cost reduction. But for most commercial metal AM, the build time and post-processing cost are significant — and a highly organic TO result may increase post-processing time enough to offset the material savings. Evaluate total cost, not just material mass.

Validated weight savings: what the data shows

Published data from production AM programs provides a realistic expectation for TO benefits:

The 30–50% range for aerospace structural brackets is well-supported. Medical implant savings are more modest because the constraints (osseointegration surface, cortical bone modulus matching) limit how much material can be removed.

Note that these figures represent the combination of TO with AM — not TO alone. In some cases, the mass reduction comes partly from removing manufacturing-driven design features (wall thickness for machineability, draft angles for casting) rather than structural TO. AM enables you to remove these manufacturing margins; TO tells you which structural material can also be removed.

Related tools and further reading

• Orientation advisor — critical input to TO workflow: determine build direction before running TO
• Support volume estimator — check whether the TO result introduces excessive support requirements
• DfAM checklist — validate the post-TO geometry before submitting for build
• Design for Metal AM — DfAM fundamentals: overhang angles, minimum wall, channel geometry
• Support structure design — detailed guide to support design for the overhangs that TO does not eliminate