On Topology Optimisation Methods and Additive Manufacture for Satellite Structures: A Review
Abstract
:1. Introduction
2. Topology Optimisation Methods
- Continuum approaches, which are based on the modification of continuous parameters such as mass density.
- Discrete approaches, which are based on the elimination or addition of material elements in a meshing context.
- Diverse approaches, containing TO continuum and discrete approaches that are used to solve specific problems such as multi-scale TO and multi-physics TO or that try to give a novel dimension to TO problems by integrating machine learning techniques.
2.1. Topology Optimisation Continuum Approaches
2.1.1. Beginnings
2.1.2. Homogenisation Method
2.1.3. Solid Isotropic Material with Penalty Method
2.1.4. Topology Derivative
2.1.5. Level-Set Method
2.1.6. Phase-Field Method
2.2. Topology Optimisation Discrete Approaches
2.2.1. Evolutionary Structural Optimisation Methods
2.2.2. Moving Morphable Voids Method
2.2.3. Metaheuristic Topology Optimisation Methods
Genetic Algorithms
Other Metaheuristic Approaches
2.3. Diverse Approaches
2.3.1. Multi-Scale Topology Optimisation Methods
- Functionally Graded Material Topology Optimisation with Level-Set Methods [261]
2.3.2. Multi-Physics Topology Optimisation Approaches
2.3.3. Machine Learning Applied to Topology Optimisation
3. Additive Manufacture in the Context of Satellite Structures
- Material bed process: This category encompasses techniques where the material is first laid down in bulk to create a bed, upon which the actual fabrication process takes place layer-by-layer. Some common examples of this category include:
- Material deposition process: This process involves transferring material from a feed source to a substrate in order to fabricate a part directly, as opposed to forming an intermediate bed. This category is divided into the following categories:
- Solid deposition.
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- −
- −
- −
- −
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- Liquid deposition.
- Slurry deposition.
- Motionless material process: Refers to AM techniques where the material feedstock remains static and does not require active conveying or deposition to construct each layer. In processes like Two-Photon Polymerisation (2PP) and Continuous Liquid Interface Production (CLIP), the photopolymer resin is already present in a vat or container. These motionless material techniques eliminate the motion requirements of powder beds, material extrusion, or droplet jetting.
3.1. General Considerations about Additive Manufacture for Topology Optimisation-Generated Solutions
3.2. Additive Manufacture Applied to the Satellite Industry
- Primary structure, structural components, and mechanisms.
- Propulsion systems, valves, filters, pipes, injectors, combustion chambers, nozzles, tanks, and multi-functional integrated components.
- Thermal systems, involving advanced thermo-optical surfaces, pre-cooling channels and piping, multi-functional integrated components, re-entry thermal protection, and gradient-sized meshes for cryogenic coolers.
- Electronics encompassing waveguides, micro-batteries, structurally embedded wiring, and intricate metallic components.
3.3. General Mechanical Requirements for Satellite Structures
- Strength: the structure must endure the designated maximum loads without failure; it is imperative that any permanent deformations that might compromise the mission’s objectives are strictly controlled.
- Local yielding: in cases of metal structures or components, localised yielding may occur, as long as it does not induce overall permanent deformation, instability, or fatigue-related structural failure.
- Buckling: the stability (i.e., no buckling) of the structure must be verified under the prescribed design loads.
- Stiffness: stiffness requirements under specified loads and boundary conditions must be identified (stiffness is often quantified in terms of a minimum natural frequency requirement), thus preventing deformations that breach specified thresholds, gaps at joints, and dynamic interaction with other subsystems.
- Dynamic behaviour: the natural frequencies of the structure must fall within designated ranges to prevent dynamic resonance with significant excitation frequencies (e.g., fundamental frequencies of launch vehicles). Avoiding mechanical resonance is a must when TO is applied to satellite structures.
4. Cases of Study on Satellite Structures by Topology Optimisation Continuum Approaches
4.1. Homogenisation Method
Small Satellite Structural Optimisation Using Genetic Algorithm Approach
- An unspecified mathematical homogenisation technique is presented to derive equivalent properties for the sandwich structure.
- There are derived relationships between the sandwich geometries and equivalent elastic module, shear rigidity, and plate rigidity.
- The equivalences enabled feasible analysis of the sandwich properties and optimisation of its design.
4.2. Solid Isotropic Material Interpolation Method
4.2.1. Design Optimisation and Validation for Additive Manufacturing: A Satellite Bracket Application
- Stress and size constraints involving a minimum member size were performed using the SIMP method through the software Altair OptiStruct® to obtain an initial optimised bracket configuration minimising compliance.
- SIMP expressed material properties as a power law function of density to interpolate between solid and void.
- The design is subjected to progressive FEA simulations under different loads to virtually validate its performance.
- The AlSi10Mg alloy is used in SLM to fabricate the final design.
4.2.2. Topology Design of a Nanosatellite Structure with Optimal Frequency Responses Filled by Non-Uniform Lattices
- A nanosatellite box with uniform lattice panels is vibration tested to obtain target frequency response data in three orthogonal axes.
- An equivalent FE model of the box is created and density-based TO is performed using the SIMP method to maximise frequency under mass constraints.
- TO result is interpreted to design variable density lattices tailored to the load paths.
4.2.3. Topology Optimisation and Modal Analysis of Nanosatellite Structure
- A vertical partitioned conceptual nanosatellite structure is designed based on requirements.
- FE modelling and analysis are performed to evaluate strength under accelerations of 11 g’s longitudinal and 6 g’s lateral launch loads.
- TO is applied through ANSYS® to reduce mass while restricting maximum displacement and stress as constraints.
- Modal analysis determined the natural frequencies and mode shapes of the optimised structure.
4.2.4. Optimisation Design of the Spaceborne Connecting Structure for a Lightweight Space Camera
- A FE model of the chamber and the initial structure is established using Hypermesh® software.
- The elastic modulus of each element is introduced using the SIMP method, whereas the optimisation model is solved by MMA.
- Parametric models were created and solved to ensure that the overall shape and dimensions of the topology remained consistent.
- A sensitivity analysis is conducted by employing a design of experiment approach to assess how size parameters impact the performance of the camera.
- Engineering analysis (static and dynamic) and performance comparison are realised.
4.2.5. Optimum Design of the Support Structure of the CMG Based on CAE
- Study of facets of the support structure of the CMG with the ANSYS® FEM software package.
- The 3D models of the CMG are established based on the optimisation.
- Vibration tests to validate the optimised design.
4.2.6. Multi-Scale Design and Optimisation for Solid-Lattice Hybrid Structures and Their Application to Aerospace Vehicle Components
- Create a solid model and define design domain.
- Establish finite mesh model and impose boundary conditions.
- Reconstruct and lattice infill.
- Perform size optimisation and verify its convergence.
4.2.7. An Aerospace Bracket Designed by Thermo-Elastic Topology Optimisation and Manufactured by Additive Manufacturing
- A thermo-elastic TO formulation is proposed to minimise compliance under displacement, volume, and thermal load constraints.
- The Rational Approximation of Material Properties (RAMP) scheme is used for material interpolation. RAMP expressed the Young’s modulus, thermal stress coefficient, and thermal conductivity of the density variables.
- Sensitivity analysis is derived for the coupled thermo-elastic response and RAMP material properties.
- An 18.3% reduction in bracket mass is achieved while satisfying all stiffness, strength, and displacement constraints.
- Mechanical testing validates the performance of the additively manufactured bracket under extreme loads (see Figure 7).
- The paper demonstrates an effective integrated approach combining TO (RAMP method) and AM for aerospace applications.
4.3. Level-Set Methods
A Level- Set-Based Topology Optimisation Approach for Thermally Radiating Structures
- To define the level-set function to implicitly represent structural boundaries.
- To construct augmented Lagrangian with volume constraint.
- To derive shape sensitivity Lagrangian using adjoint method.
- To solve state equations for and adjoint state q*.
- To construct velocity field from the shape sensitivity analysis.
- To solve the Hamilton–Jacobi equation to evolve the level set based on .
- To re-initialise periodically as signed distance function.
- To iterate steps (iii) to (vii) until convergence.
- To extract final structure shape .
- To validate the approach on a 2D aluminium plate with dimensions of 100 cm × 100 cm × 1 cm.
4.4. Other Topology Optimisation Applications on Satellite Secondary Structures
5. Cases of Study on Satellite Structures by Topology Optimisation Discrete Approaches
5.1. Metaheuristic Methods
5.1.1. Parallel Optimal Design of Satellite Bus Structures Using Particle Swarm Optimisation
- The use of the PSO algorithm is suitable for problems with expensive function evaluations that can be easily parallelised.
- The use of a grid-computing framework to distribute simulation jobs for automatic mesh generation in FEA.
- The use of MSC Patran® 2004 and MSC Nastran® 2004 (commercial software) for meshing and analysis.
- The PSO algorithm module coordinated job submission and gathered results from the grid resources.
- Optimisation is performed in two stages: an initial optimisation execution, and then, a reinforcement is added to address constraint violations. Then, a second optimisation is performed.
- Optimisation of a 32-variable adaptor-ring model, reducing its mass 54% from 26.2 kg to 12.4 kg.
- Performed optimisation in two stages:
- Optimised to 13.6 kg mass before violating constraints.
- Reinforced model and re-optimised to satisfy constraints mentioned above.
- A 60-node grid is leveraged to complete 1266 minutes of computations.
- Sensitivity analyses were conducted to study the impact of parameters on the optimised design.
5.1.2. Structural Optimisation Design of Shock Isolation Ring for Satellite–Rocket Separation
- A shock response spectrum synthesis to obtain a transient time domain shock load is used.
- A FE model of the shock isolation ring structure in Catia®, Abaqus® and Matlab®.
- An objective function is defined by designing the variables and constraints mentioned above; mass minimisation is intended.
- Response surface models for shock isolation ratio and strength based on FEA at sample points are built.
- Adaptive simulated annealing algorithm to solve the mixed discrete-continuous optimisation problem is used.
- Computed sensitivities of objectives and constraints to design variables at the optimal design.
5.1.3. Small Satellite Structural Optimisation Using Genetic Algorithm Approach
5.1.4. The Topology Optimisation of Electronic Parts Mounted on Microsatellite
- Apply auto-positioning method: Components are placed on the board from upper left to right with an established distance between parts for a given pattern. In case a component crosses the right edge of the board, it is placed on the left edge below previously placed parts.
- Placement is evaluated with an autorouting function.
- The design variables are obtained from the evolutionary computation by MOGA with 70 generations to evolve. The established objective functions are to minimise board area and maximise autorouting rate.
5.1.5. An Engineering Method for Complex Structural Optimisation Involving Both Size and Topology Design Variables
- The structural and sensitivity analysis of the initial design is carried out.
- The first-level problem is approximated by a Branched Multi-Point Approximation (BMA) function.
- Optimisation of discrete variables through a GA; if the problem is not convergent, it is repeated from the structural analysis.
- The second-level problem for the optimisation of continuous variables is approached and solved by means of the dual method for the calculation of the individual amplitude.
5.2. Other Topology Optimisation Applications on Satellite Secondary Structures
6. Discussion and Conclusions
6.1. Topology Optimisation Methods
- Homogenisation methods are difficult to use, especially when implemented for 3D TO problems. Nonetheless, multi-scale approaches make use of them.
- SIMP methods require selecting an appropriate penalisation factor.
- LSMs are sensitive to initial solution guesses.
- Topological derivative methods are mathematically complicated.
- The BESO method is sensitive to ER-selected value.
- MVV is an interesting alternative approach but requires more development.
- Metaheuristic approaches lack consistent development. There is a large variety of methods and implementations but very few of them have seen active development. Additionally, a large number of function evaluations are required in metaheuristic approaches. Nonetheless, metaheuristic approaches allow flexible objective functions that allow the combination of discrete and continuous design variables.
- Machine learning approaches do not scale well to three-dimensional design space. An important number of implementations requires large amounts of previously optimised cases to work. Additionally, very few approaches are “physics informed”, nonetheless they are very promising and will see important development in the years to come.
6.2. Additive Manufacture Processes
- Length scale is necessary to eliminate tiny (not manufacturable) features.
- Thermal gradients, residual stresses, and anisotropy need to be addressed when TO solutions are intended to be manufactured.
- Requirements for supporting structures must be met in the AM fabrication process.
- Adequate control in machine parameters must be met to ensure repeatability.
6.3. Cases of Study for TO Methods Applied to Satellite Structures
- There is little support from FEA available software for the implementation of customised TO algorithms.
- FEA’s available software for TO tools does not report implemented algorithms and/or parameters to the final user, hindering the possibility of proper comparisons between scholars.
- There is a need for support structures in metal AM processes such as SLM to print overhangs and bridges. This adds mass and requires post-processing to remove supports.
- Achieving the necessary surface finishes for satellite components can pose a challenge due to the roughness resulting from AM. Typically, extra finishing processes are needed.
- Lack of design standards for AM satellite components, especially for structural parts and mechanisms. Current international regulations have not been aimed at encompassing all the AM methods [343,345]. Moreover, in the absence of robust AM regulations, the oversight of international regulations within the aerospace field has received even less attention and the few standards that do exist for certain methods [529] (refs. [530,531,532,533,534] under development are focused on administrative or other non-pertinent issues that are not related to AM. Even though NASA has published some standards such as Laser Powder Bed Fusion methods [535,536] and general requirements [537].
- It is essential to recognise and certify novel AM alloys and methods for diverse satellite uses, as material characteristics may differ among various AM machines and methods.
6.4. Addressing Natural Frequency as Part of the TO Problem
6.5. Multi-Scale Approaches on Satellite TO
6.6. Multi-Physics Approaches to Satellite TO
6.7. Final Remarks
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
Abbreviations
2PP | Two-Photon Polymerisation |
3DGP | 3D Gel Printing |
AM | Additive Manufacture |
ASTM | American Society for Testing and Materials |
BESO | Bi-Directional ESO |
BJ3DP | Binder Jetting 3D Printing |
BMA | Branched Multi-Point Approximation |
EBM | Electron Beam Melting |
ESO | Evolutionary Structural Optimisation |
CAD | Computer-Aided Design |
CISM | Centre for Mechanical Sciences |
CLF | Ceramic Laser Fusion |
CLIP | Continuous Liquid Interface Production |
CNC | Computerised Numerical Control |
CMG | Control Moment Gyroscope |
DED | Direct Energy Deposition |
DLP | Digital Light Processing |
DMD | Direct Metal Deposition |
FE | Finite Element |
FEA | Finite Element Analysis |
FEM | Finite Element Method |
FFF | Fused Filament Fabrication |
GAs | Genetic Algorithms |
GEO | GeoStationary Orbit |
HSS | High-Speed Sintering |
IGA | Iso-Geometric Analysis |
IJP | Ink Jet Printing |
LEO | Low Earth Orbit |
LOS | Line of Sight |
LSM | Level-Set Method |
MMA | Method of Moving Asymptotes |
MMC | Moving Morphable Components |
MMV | Moving Morphable Voids |
NASA | National Aeronautics and Space Administration |
PAM | Plasma Arc Additive Manufacturing |
PJ | Photopolymer Jetting |
PSO | Particle Swarm Optimisation |
RAMP | Rational Approximation of Material Properties |
RFP | Rapid Freeze Prototyping |
SIMP | Solid Isotropic Material with Penalty |
SLA | Stereolithography |
SLM | Selective Laser Melting |
SLS | Selective Laser Sintering |
SM | Subtractive Manufacture |
T3DP | Thermoplastic 3D Printing |
TO | Topology Optimisation |
WAAM | Wire and Arc Additive Manufacturing |
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Topology Optimisation Approaches | ||
---|---|---|
Continuum Approaches | Discrete Approaches | Diverse Approaches |
Homogenisation Method | Evolutionary Structural Optimisation (ESO) | Machine Learning Applied to TO |
Level-Set Method (LSM) | Moving Morphable Voids (MMV) | Multi-Physics TO |
Phase-Field Method | Soft-Kill Bidirectional ESO (SBESO) | Multi-Scale TO |
Solid Isotropic Material with Penalty (SIMP) | Metaheuristic Algorithms | |
Topology Derivative Method | Metaheuristic Hybrid Algorithms |
Metaheuristic Algorithms | ||
---|---|---|
Ant Colony Algorithm | Electro-Search Algorithm | Simulated Annealing (SA) |
Artificial Immune System Algorithm | Firefly Algorithm | Symbiotic Organisms Search Algorithm |
Bacterial Chemotaxis | Genetic Algorithms (GAs) | Plasma Generation Algorithm |
Bat Algorithm | Harmony Search (HS) | |
Differential Evolution | Particle Swarm (PSO) |
Metaheuristic Hybrid Algorithms | ||
---|---|---|
ESO with GA | BESO with HS | BESO with SA |
BESO with GA | BESO with PSO | SIMP with a GA |
Ni-Base | Fe-Base | Cu-Base | Al-Base | Refractory | Ti-Base | Co-Base | Bimetalic |
---|---|---|---|---|---|---|---|
Inconel 625 | SS 17-4PH | GRCop-84 | AlSi10Mg | W | Ti6Al4V | CoCr | GRCop-84/IN625 |
Inconel 718 | SS 15-5 GP1 | GRCop-42 | A205 | W-25Re | -TiAl | Stellite 6 | C18150/IN625 |
Hastelloy-X | SS 304L | C18150 | F357 | Mo | Ti-6–2-4–2 | Stellite 21 | |
Haynes 230 | SS 316L | C18200 | 2024 | Mo-41Re | Haynes 188 | ||
Haynes 214 | SS 420 | Glidcop | 4047 | Mo-47.5Re | |||
Haynes 282 | Tool Steel (4140/4340) | CU110 | 6061 | C-103 | |||
Monel K-500 | Invar 36 | 7050 | Ta | ||||
C-276 | SS347 | ||||||
Rene 80 | JBK-75 | ||||||
Waspalloy | NASA HR- 1 |
Acceleration (Hz) | Frequency (Hz) | Square Root of the Sum of the Squares | |
---|---|---|---|
X-axis | 20 | 112 | 24.4 |
Y-axis | 10 | 138 | 24.4 |
Z-axis | 8.7 | 148 | 18.9 |
Zone | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
---|---|---|---|---|---|---|---|---|---|---|
Lower bound (mm) | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |
Initial value (mm) | 5 | 5 | 5 | 15 | 10 | 5 | 5 | 5 | 10 | 10 |
Upper bound (mm) | 10 | 10 | 10 | 15 | 10 | 10 | 10 | 10 | 10 | 10 |
Optimised value (mm) | 8.5 | 9 | 5 | 15 | 10 | 4 | 5 | 8 | 3 | 7.5 |
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Hurtado-Pérez, A.B.; Pablo-Sotelo, A.d.J.; Ramírez-López, F.; Hernández-Gómez, J.J.; Mata-Rivera, M.F. On Topology Optimisation Methods and Additive Manufacture for Satellite Structures: A Review. Aerospace 2023, 10, 1025. https://doi.org/10.3390/aerospace10121025
Hurtado-Pérez AB, Pablo-Sotelo AdJ, Ramírez-López F, Hernández-Gómez JJ, Mata-Rivera MF. On Topology Optimisation Methods and Additive Manufacture for Satellite Structures: A Review. Aerospace. 2023; 10(12):1025. https://doi.org/10.3390/aerospace10121025
Chicago/Turabian StyleHurtado-Pérez, Arturo Benjamín, Abraham de Jesús Pablo-Sotelo, Fabián Ramírez-López, Jorge Javier Hernández-Gómez, and Miguel Felix Mata-Rivera. 2023. "On Topology Optimisation Methods and Additive Manufacture for Satellite Structures: A Review" Aerospace 10, no. 12: 1025. https://doi.org/10.3390/aerospace10121025