Periodic Reporting for period 1 - NOVITAS (Nonlinear analysis for virtual design of composite deployable space booms and membranes)
Période du rapport: 2023-03-15 au 2025-03-14
The project’s unique blend of theoretical modeling, experimental validation, and numerical implementation will yield a pioneering virtual design tool for deployable structures. This tool will have broad applicability for satellites, space telescopes, communication arrays, and other orbiting platforms. By improving the packaging efficiency, mass savings, and deployment reliability of large space systems, NOVITAS directly supports strategic goals for more sustainable and ambitious space exploration. Larger deployable antennas, high-precision telescopes, and solar sails will, for instance, enable better data collection for Earth observation, climate monitoring, and space-based solar power. The results will facilitate lower mission costs, increased commercial viability of new space ventures, and faster innovation cycles in the “New Space” industry. Improved satellite capabilities have downstream benefits for society as they support applications in environmental risk management, resource monitoring, and global communication. As the demand grows for advanced Earth observation tools (e.g. for climate change assessments) and deep-space science missions, policy makers in Europe and elsewhere emphasize improved reliability and reduced cost of access to space. By offering validated approaches to packaging and deploying large structures in small launch vehicles, NOVITAS addresses both commercial and scientific priorities, reinforcing Europe’s strategic autonomy in space.
While NOVITAS is primarily rooted in aerospace engineering, material science, and applied mathematics, the human dimension is reflected in its societal and environmental impacts. The project’s outcomes are intimately tied to societal decision-making and policy frameworks. Collaboration with experts in science communication or technology policy could further illuminate the best practices for implementing next-generation space technology in a socially responsible way, ensuring that the engineering breakthroughs align with overarching humanistic, ethical, and environmental considerations.
While NOVITAS is primarily rooted in aerospace engineering, material science, and applied mathematics, the human dimension is reflected in its societal and environmental impacts. The project’s outcomes are intimately tied to societal decision-making and policy frameworks. Collaboration with experts in science communication or technology policy could further illuminate the best practices for implementing next-generation space technology in a socially responsible way, ensuring that the engineering breakthroughs align with overarching humanistic, ethical, and environmental considerations.
The conducted activities centered on the numerical simulation of folding and deployment processes in deployable structures, with particular attention to Triangular Rollable And Collapsible (TRAC) longerons used in the Space-Based Solar Power Project (SSPP). These ultra-thin composite components (thicknesses of 0.2 mm and 0.1 mm) serve as the structural frame in a constellation of solar arrays designed to collect solar energy in space and beam it to Earth.
Folding Simulation:
Initially, the focus was on modeling the folding of a 400 mm TRAC longeron. Because its cross-section includes curved domains, contact arises among various parts of the longeron, requiring a specialized contact algorithm. To address this, a novel contact mechanics approach was developed using a node-to-surface model with nonlinear springs. The stiffness parameters of these springs were optimized to minimize computational time, ensuring an efficient simulation of the folding phase.
Next, the same methodology was applied to a more complex “strip” configuration, which consists of two TRAC longerons connected by transverse elements (battens). Since the strip forms the basic module of the SSPP structures, accurate simulation of its folding is crucial. Adopting the same geometric and contact nonlinear formulation, a 400 mm strip was folded successfully. Its performance was benchmarked against Abaqus simulations, demonstrating very close agreement in both deformed shapes and curvature values. Moreover, computational time was more than halved compared to the explicit approach in Abaqus, thanks to an implicit scheme that overcomes Abaqus’ known difficulties with implicit contact simulations. By leveraging the Carrera Unified Formulation (CUF), the thickness of these thin-walled components could be rigorously accounted for without incurring the usual aspect-ratio limitations of commercial finite element packages. This enabled the simulation of longer assemblies—up to 1 m and 5 m—with reliable accuracy.
Deployment Simulation:
Subsequently, the study turned to the deployment phase, which occurs almost instantaneously (on the order of 0.01 seconds) due to the internal release of stored strain energy. A nonlinear dynamic analysis based on the Newmark HHT-α method was thus integrated into the simulation procedure. The overall process was twofold:
1) A nonlinear static analysis captured the folding of the strip and established an equilibrium configuration.
2) A nonlinear dynamic analysis then simulated the rapid deployment from that equilibrium state.
These simulations were validated through experimental data and by comparison with Abaqus (running an explicit formulation). The numerical results matched the experimental measurements of folding angle evolution over time, as well as energy trends obtained from Abaqus. Crucially, all of this was accomplished using an implicit formulation, which is significantly more time-efficient in CUF-based simulations than an explicit approach, given the extremely small time steps required for explicit schemes when very thin structural components are modeled in full 3D.
Dynamic Response and Local Buckling:
Finally, an experimental and numerical investigation was conducted to determine if dynamic excitations during operation induce local buckling in TRAC longerons and, if so, whether such buckling increases damping. Two boundary configurations were tested using sine sweep experiments at increasing amplitudes. In the first configuration (where flanges were unconstrained), no local buckling was observed, and the damping ratio remained low. In the second configuration (with both flanges and web fully clamped), local buckling occurred at higher amplitudes, leading to a marked increase in the measured damping ratio.
A complementary numerical analysis employed CUF-based refined one-dimensional finite elements, enabling an accurate representation of the longeron’s complex geometry with drastically reduced computational costs. Nonlinear dynamic simulations were performed using the Newmark algorithm and the Hilbert-Hughes-Taylor (HHT) method, applying high numerical damping to ensure convergence. Two types of simulations were examined: one neglecting structural damping altogether, and another incorporating Rayleigh-type damping parameters derived from the experiments. The results showed that excluding structural damping led to unreliable predictions of damping ratio evolution, while the model that included Rayleigh damping accurately captured the experimental response. These findings highlight the critical importance of incorporating structural damping for realistic simulations of the dynamic behavior of TRAC longerons.
Outcomes and Main Achievements:
1) Efficient Folding Simulation: Introduction of a novel contact mechanics formulation significantly reduced computational time and allowed implicit simulations of complex folded structures.
2) Advanced Deployment Modeling: Successful implementation of a nonlinear dynamic approach based on the Newmark HHT-α method, validated by both experiments and Abaqus simulations.
3) Large-Scale Analysis via CUF: CUF-based refined finite elements overcame typical aspect-ratio constraints, enabling analyses of longer specimens (up to 5 m).
4) Damping and Local Buckling Insights: Experiments showed that local buckling in TRAC longerons can dramatically increase damping, a phenomenon accurately reproduced only when structural damping was included in the numerical model.
Overall, these results confirm the reliability of the implicit CUF-based framework for modeling deployable structures. The combination of validated contact algorithms, nonlinear dynamics, and a robust damping formulation will be instrumental in designing and analyzing future SSPP deployable systems with greater efficiency and accuracy.
Folding Simulation:
Initially, the focus was on modeling the folding of a 400 mm TRAC longeron. Because its cross-section includes curved domains, contact arises among various parts of the longeron, requiring a specialized contact algorithm. To address this, a novel contact mechanics approach was developed using a node-to-surface model with nonlinear springs. The stiffness parameters of these springs were optimized to minimize computational time, ensuring an efficient simulation of the folding phase.
Next, the same methodology was applied to a more complex “strip” configuration, which consists of two TRAC longerons connected by transverse elements (battens). Since the strip forms the basic module of the SSPP structures, accurate simulation of its folding is crucial. Adopting the same geometric and contact nonlinear formulation, a 400 mm strip was folded successfully. Its performance was benchmarked against Abaqus simulations, demonstrating very close agreement in both deformed shapes and curvature values. Moreover, computational time was more than halved compared to the explicit approach in Abaqus, thanks to an implicit scheme that overcomes Abaqus’ known difficulties with implicit contact simulations. By leveraging the Carrera Unified Formulation (CUF), the thickness of these thin-walled components could be rigorously accounted for without incurring the usual aspect-ratio limitations of commercial finite element packages. This enabled the simulation of longer assemblies—up to 1 m and 5 m—with reliable accuracy.
Deployment Simulation:
Subsequently, the study turned to the deployment phase, which occurs almost instantaneously (on the order of 0.01 seconds) due to the internal release of stored strain energy. A nonlinear dynamic analysis based on the Newmark HHT-α method was thus integrated into the simulation procedure. The overall process was twofold:
1) A nonlinear static analysis captured the folding of the strip and established an equilibrium configuration.
2) A nonlinear dynamic analysis then simulated the rapid deployment from that equilibrium state.
These simulations were validated through experimental data and by comparison with Abaqus (running an explicit formulation). The numerical results matched the experimental measurements of folding angle evolution over time, as well as energy trends obtained from Abaqus. Crucially, all of this was accomplished using an implicit formulation, which is significantly more time-efficient in CUF-based simulations than an explicit approach, given the extremely small time steps required for explicit schemes when very thin structural components are modeled in full 3D.
Dynamic Response and Local Buckling:
Finally, an experimental and numerical investigation was conducted to determine if dynamic excitations during operation induce local buckling in TRAC longerons and, if so, whether such buckling increases damping. Two boundary configurations were tested using sine sweep experiments at increasing amplitudes. In the first configuration (where flanges were unconstrained), no local buckling was observed, and the damping ratio remained low. In the second configuration (with both flanges and web fully clamped), local buckling occurred at higher amplitudes, leading to a marked increase in the measured damping ratio.
A complementary numerical analysis employed CUF-based refined one-dimensional finite elements, enabling an accurate representation of the longeron’s complex geometry with drastically reduced computational costs. Nonlinear dynamic simulations were performed using the Newmark algorithm and the Hilbert-Hughes-Taylor (HHT) method, applying high numerical damping to ensure convergence. Two types of simulations were examined: one neglecting structural damping altogether, and another incorporating Rayleigh-type damping parameters derived from the experiments. The results showed that excluding structural damping led to unreliable predictions of damping ratio evolution, while the model that included Rayleigh damping accurately captured the experimental response. These findings highlight the critical importance of incorporating structural damping for realistic simulations of the dynamic behavior of TRAC longerons.
Outcomes and Main Achievements:
1) Efficient Folding Simulation: Introduction of a novel contact mechanics formulation significantly reduced computational time and allowed implicit simulations of complex folded structures.
2) Advanced Deployment Modeling: Successful implementation of a nonlinear dynamic approach based on the Newmark HHT-α method, validated by both experiments and Abaqus simulations.
3) Large-Scale Analysis via CUF: CUF-based refined finite elements overcame typical aspect-ratio constraints, enabling analyses of longer specimens (up to 5 m).
4) Damping and Local Buckling Insights: Experiments showed that local buckling in TRAC longerons can dramatically increase damping, a phenomenon accurately reproduced only when structural damping was included in the numerical model.
Overall, these results confirm the reliability of the implicit CUF-based framework for modeling deployable structures. The combination of validated contact algorithms, nonlinear dynamics, and a robust damping formulation will be instrumental in designing and analyzing future SSPP deployable systems with greater efficiency and accuracy.
Results Overview and Novelty
1) First-Time Code Implementations:
- CUF-Based Simulations: For the first time, a CUF-based approach was employed to analyze realistic space-deployable structures, providing highly accurate results while overcoming typical aspect-ratio constraints in conventional finite element packages.
- Contact Formulation: A novel contact algorithm was introduced, employing nonlinear springs to reduce computational cost and enable both implicit (static and dynamic) and explicit dynamic simulations in a single unified framework. This is unprecedented in the code used.
2) Validation and Comparison:
- The simulations matched experimental data and results from well-established commercial software (e.g. Abaqus) in terms of folded shapes, deformation histories, and dynamic responses.
- The newly implemented implicit static, implicit dynamic, and explicit dynamic schemes were appropriately calibrated to handle contact with minimal computational overhead.
3) Micro-Buckling and Damping Insights:
- Recent experiments revealed that micro-buckling in TRAC longerons adds notable damping to the system’s dynamic response. This finding was quantified and can be leveraged in future designs for enhanced vibration control and stability in deployable space structures.
Potential Impacts
1) Advanced Design Capabilities: The demonstrated accuracy and reduced computational times open the door to more complex and cost-effective design studies of large deployable structures for space applications.
2) Greater Reliability: By integrating this new contact formulation with CUF, designers can efficiently predict not only the static/folding behavior but also the dynamic deployment and post-deployment performance of ultra-thin composite structures.
3) Improved Structural Damping: The identified phenomenon of micro-buckling-induced damping provides a valuable avenue for fine-tuning the dynamic behavior of deployable systems. In future projects, this could lead to more robust structures that can better withstand high-frequency loads and vibrations.
Key Needs for Further Uptake and Success
1) Further Research and Demonstration:
- Additional experimental campaigns, especially on larger-scale prototypes, will strengthen confidence in the new CUF-based methods and validate the impact of micro-buckling on a wider range of deployable systems.
2) Access to Markets and Finance:
- Funding mechanisms are needed to move from laboratory testing to demonstrators and eventually to full-scale in-orbit validation.
- Partnerships with aerospace and energy-sector stakeholders can accelerate commercial adoption.
3) Commercialisation and IPR Support:
- Secure intellectual property protection for the newly developed algorithms and contact implementations to foster technology transfer and commercial exploitation.
- Open pathways for licensing or collaboration with commercial software vendors.
4) International Collaboration and Standardisation:
- Engaging with regulatory bodies and standardisation committees (e.g. for space structures) will be crucial to incorporate new guidelines that reflect the advantages and reliability of CUF-based simulations.
- Global partnerships can help harmonize methods and promote widespread adoption.
5) Continued Code Development:
- Ongoing refinement of the nonlinear spring stiffness calibration and dynamic solvers will expand the range of applications.
- Efforts to enhance user-friendliness and computational efficiency will facilitate broader use across industry and academia.
Conclusion
This work establishes a pioneering framework for analyzing deployable space structures using CUF, implicit/explicit dynamic formulations, and a novel contact approach. The validated simulations and insights into micro-buckling-induced damping significantly advance the state of the art, laying a solid foundation for future research, commercialisation, and potentially transformative space applications.
1) First-Time Code Implementations:
- CUF-Based Simulations: For the first time, a CUF-based approach was employed to analyze realistic space-deployable structures, providing highly accurate results while overcoming typical aspect-ratio constraints in conventional finite element packages.
- Contact Formulation: A novel contact algorithm was introduced, employing nonlinear springs to reduce computational cost and enable both implicit (static and dynamic) and explicit dynamic simulations in a single unified framework. This is unprecedented in the code used.
2) Validation and Comparison:
- The simulations matched experimental data and results from well-established commercial software (e.g. Abaqus) in terms of folded shapes, deformation histories, and dynamic responses.
- The newly implemented implicit static, implicit dynamic, and explicit dynamic schemes were appropriately calibrated to handle contact with minimal computational overhead.
3) Micro-Buckling and Damping Insights:
- Recent experiments revealed that micro-buckling in TRAC longerons adds notable damping to the system’s dynamic response. This finding was quantified and can be leveraged in future designs for enhanced vibration control and stability in deployable space structures.
Potential Impacts
1) Advanced Design Capabilities: The demonstrated accuracy and reduced computational times open the door to more complex and cost-effective design studies of large deployable structures for space applications.
2) Greater Reliability: By integrating this new contact formulation with CUF, designers can efficiently predict not only the static/folding behavior but also the dynamic deployment and post-deployment performance of ultra-thin composite structures.
3) Improved Structural Damping: The identified phenomenon of micro-buckling-induced damping provides a valuable avenue for fine-tuning the dynamic behavior of deployable systems. In future projects, this could lead to more robust structures that can better withstand high-frequency loads and vibrations.
Key Needs for Further Uptake and Success
1) Further Research and Demonstration:
- Additional experimental campaigns, especially on larger-scale prototypes, will strengthen confidence in the new CUF-based methods and validate the impact of micro-buckling on a wider range of deployable systems.
2) Access to Markets and Finance:
- Funding mechanisms are needed to move from laboratory testing to demonstrators and eventually to full-scale in-orbit validation.
- Partnerships with aerospace and energy-sector stakeholders can accelerate commercial adoption.
3) Commercialisation and IPR Support:
- Secure intellectual property protection for the newly developed algorithms and contact implementations to foster technology transfer and commercial exploitation.
- Open pathways for licensing or collaboration with commercial software vendors.
4) International Collaboration and Standardisation:
- Engaging with regulatory bodies and standardisation committees (e.g. for space structures) will be crucial to incorporate new guidelines that reflect the advantages and reliability of CUF-based simulations.
- Global partnerships can help harmonize methods and promote widespread adoption.
5) Continued Code Development:
- Ongoing refinement of the nonlinear spring stiffness calibration and dynamic solvers will expand the range of applications.
- Efforts to enhance user-friendliness and computational efficiency will facilitate broader use across industry and academia.
Conclusion
This work establishes a pioneering framework for analyzing deployable space structures using CUF, implicit/explicit dynamic formulations, and a novel contact approach. The validated simulations and insights into micro-buckling-induced damping significantly advance the state of the art, laying a solid foundation for future research, commercialisation, and potentially transformative space applications.