Transactions of Nanjing University of Aeronautics & Astronautics
Issue 3,2026 Table of Contents
2026(3):317-339.
DOI: 10.16356/j.1005-1120.2026.03.001
Abstract:
Continuous fiber-reinforced metal matrix composites （CFMMCs） exhibit exceptional specific strength and high-temperature resistance， making them ideal for aerospace applications. However， their anisotropic and heterogeneous structure lead to severe machining challenges， including tool wear， fiber pull-out， and interfacial debonding. This review summarizes the current state of CFMMCs machining， emphasizing the role of energy field-assisted machining and their limitations. Conventional machining （CM） exhibits complex material removal mechanisms involving plastic deformation， brittle fracture， and interface failure. Ultrasonic vibration-assisted machining （UVAM） reduces cutting forces and residual stress through acoustic softening， while laser-assisted machining （LAM） induces fiber ductile transition and matrix softening. Femtosecond laser machining further enables high-precision， low-damage ablation. Despite these advances， research gaps remain regarding anisotropic effects， parameter coordination， and damage-service life relationships. The development of multi-energy field synergy， AI-based closed-loop control， and integrated additive-subtractive platforms is also analyzed. Finally， based on the current development status and the requirements of aerospace manufacturing， future trends in CFMMCs machining are proposed.
Continuous fiber-reinforced metal matrix composites （CFMMCs） exhibit exceptional specific strength and high-temperature resistance， making them ideal for aerospace applications. However， their anisotropic and heterogeneous structure lead to severe machining challenges， including tool wear， fiber pull-out， and interfacial debonding. This review summarizes the current state of CFMMCs machining， emphasizing the role of energy field-assisted machining and their limitations. Conventional machining （CM） exhibits complex material removal mechanisms involving plastic deformation， brittle fracture， and interface failure. Ultrasonic vibration-assisted machining （UVAM） reduces cutting forces and residual stress through acoustic softening， while laser-assisted machining （LAM） induces fiber ductile transition and matrix softening. Femtosecond laser machining further enables high-precision， low-damage ablation. Despite these advances， research gaps remain regarding anisotropic effects， parameter coordination， and damage-service life relationships. The development of multi-energy field synergy， AI-based closed-loop control， and integrated additive-subtractive platforms is also analyzed. Finally， based on the current development status and the requirements of aerospace manufacturing， future trends in CFMMCs machining are proposed.
2026(3):340-355.
DOI: 10.16356/j.1005-1120.2026.03.002
Abstract:
A hybrid action deformation control method based on hybrid proximal policy optimization （HPPO） is proposed for titanium alloy structural components. Existing reinforcement learning algorithms are generally confined to either discrete or continuous action spaces， and thus cannot simultaneously optimize machining sequence and allowance. The proposed method unifies both decision variables—machining sequence as discrete actions and machining allowance as continuous parameters—into a single parameterized hybrid action space. Online deformation force monitoring data serve as state feedback to enable adaptive control under dynamic machining conditions. A dual-layer reward mechanism combining process-level deformation force uniformity with terminal deformation convergence is designed to guide the agent toward synchronized suppression of both local and global deformations. Experimental validation on a Ti6Al4V aviation structural component demonstrates that the proposed method reduces average machining deformation from 0.103 mm to 0.054 mm， with RMSE decreasing from 0.119 mm to 0.071 mm， representing a 47.57% reduction relative to the uncontrolled case. These results confirm the accuracy and effectiveness of the proposed method in real manufacturing environments.
A hybrid action deformation control method based on hybrid proximal policy optimization （HPPO） is proposed for titanium alloy structural components. Existing reinforcement learning algorithms are generally confined to either discrete or continuous action spaces， and thus cannot simultaneously optimize machining sequence and allowance. The proposed method unifies both decision variables—machining sequence as discrete actions and machining allowance as continuous parameters—into a single parameterized hybrid action space. Online deformation force monitoring data serve as state feedback to enable adaptive control under dynamic machining conditions. A dual-layer reward mechanism combining process-level deformation force uniformity with terminal deformation convergence is designed to guide the agent toward synchronized suppression of both local and global deformations. Experimental validation on a Ti6Al4V aviation structural component demonstrates that the proposed method reduces average machining deformation from 0.103 mm to 0.054 mm， with RMSE decreasing from 0.119 mm to 0.071 mm， representing a 47.57% reduction relative to the uncontrolled case. These results confirm the accuracy and effectiveness of the proposed method in real manufacturing environments.
2026(3):356-370.
DOI: 10.16356/j.1005-1120.2026.03.003
Abstract:
To address the insufficient interlayer mechanical properties of glass fiber-reinforced polyetheretherketone （GF/PEEK） composites fabricated by fused deposition modeling （FDM）， resulting from the impracticality of post-process heat treatment for large-scale components and structural circuit-integrated components， an in situ thermal radiation-assisted strengthening method was proposed to enhance the interlayer mechanical properties along the build direction. The mechanical properties and interlayer strengthening mechanism of GF/PEEK composites under different thermal treatment strategies were systematically investigated by regulating the chamber temperature and in situ thermal radiation power， combined with tensile tests， interlayer tensile tests， and fracture surface morphology analysis. The results showed that increasing the chamber temperature improved the tensile properties in the horizontal direction. At a chamber temperature of 200 ℃， the tensile strength and Young’s modulus reached 62.72 MPa and 3.45 GPa， respectively. However， the interlayer tensile strength decreased from 20.61 MPa to 6.03 MPa， while the interlayer Young’s modulus increased from 1.90 GPa to 2.24 GPa. By contrast， in situ thermal radiation significantly enhanced the interlayer mechanical properties of specimens fabricated along the build direction. At a thermal radiation power of 255 W， the vertical tensile strength and fracture elongation increased to 2.34 and 7.91 times those of conventional FDM specimens， respectively， achieving mechanical properties comparable to those of post-process heat-treated specimens. Fracture surface analysis further revealed that in situ thermal radiation promoted interlayer polymer chain diffusion and molecular entanglement while reducing interfacial defects， thereby substantially improving the interlayer bonding performance. The proposed method effectively enhances the interlayer mechanical properties of FDM-fabricated GF/PEEK composites without requiring an additional post-process heat treatment， providing an effective processing strategy for the additive manufacturing of high-performance thermoplastic composite structures.
To address the insufficient interlayer mechanical properties of glass fiber-reinforced polyetheretherketone （GF/PEEK） composites fabricated by fused deposition modeling （FDM）， resulting from the impracticality of post-process heat treatment for large-scale components and structural circuit-integrated components， an in situ thermal radiation-assisted strengthening method was proposed to enhance the interlayer mechanical properties along the build direction. The mechanical properties and interlayer strengthening mechanism of GF/PEEK composites under different thermal treatment strategies were systematically investigated by regulating the chamber temperature and in situ thermal radiation power， combined with tensile tests， interlayer tensile tests， and fracture surface morphology analysis. The results showed that increasing the chamber temperature improved the tensile properties in the horizontal direction. At a chamber temperature of 200 ℃， the tensile strength and Young’s modulus reached 62.72 MPa and 3.45 GPa， respectively. However， the interlayer tensile strength decreased from 20.61 MPa to 6.03 MPa， while the interlayer Young’s modulus increased from 1.90 GPa to 2.24 GPa. By contrast， in situ thermal radiation significantly enhanced the interlayer mechanical properties of specimens fabricated along the build direction. At a thermal radiation power of 255 W， the vertical tensile strength and fracture elongation increased to 2.34 and 7.91 times those of conventional FDM specimens， respectively， achieving mechanical properties comparable to those of post-process heat-treated specimens. Fracture surface analysis further revealed that in situ thermal radiation promoted interlayer polymer chain diffusion and molecular entanglement while reducing interfacial defects， thereby substantially improving the interlayer bonding performance. The proposed method effectively enhances the interlayer mechanical properties of FDM-fabricated GF/PEEK composites without requiring an additional post-process heat treatment， providing an effective processing strategy for the additive manufacturing of high-performance thermoplastic composite structures.
2026(3):371-385.
DOI: 10.16356/j.1005-1120.2026.03.004
Abstract:
The deployment of unmanned aerial vehicle （UAV） hangars is critical to the efficiency of forest inspections， significantly influencing both infrastructure construction costs and operational expenses. Existing research on hangar selection often overlooks the complex constraints posed by forest environments， such as topographical variability， power limitations， and coverage demands. To tackle these challenges， this paper presents a multi-objective optimization approach for UAV hangar selection in forest environments， aiming to reduce construction costs while maximizing coverage under complex topographical constraints. The process begins with the preliminary selection of candidate hangars， utilizing geographic data such as the digital elevation model （DEM）， meteorological data， and power/signal coverage. A multi-criteria decision analysis （MCDA） method evaluates and scores candidates based on rigid and flexible criteria， including topographical suitability， wind speed， and power supply availability. A multi-objective optimization model is then developed to optimize the layout of hangars， incorporating critical constraints such as topographical characteristics， UAV power limits， and coverage redundancy. To solve this optimization problem， the non-dominated sorting genetic algorithm Ⅱ （NSGA-Ⅱ） is applied. Experimental results demonstrate that the proposed method outperforms traditional approaches， such as the greedy algorithm and the single-objective genetic algorithm. Specifically， the NSGA-Ⅱ method reduces the number of hangars by 8.3%， and increases the coverage by 1.6%. It also significantly accelerates the convergence， demonstrating superior performance and efficiency. This methodology provides a comprehensive solution for UAV deployment in forest inspections and can be adapted to other complex topography.
The deployment of unmanned aerial vehicle （UAV） hangars is critical to the efficiency of forest inspections， significantly influencing both infrastructure construction costs and operational expenses. Existing research on hangar selection often overlooks the complex constraints posed by forest environments， such as topographical variability， power limitations， and coverage demands. To tackle these challenges， this paper presents a multi-objective optimization approach for UAV hangar selection in forest environments， aiming to reduce construction costs while maximizing coverage under complex topographical constraints. The process begins with the preliminary selection of candidate hangars， utilizing geographic data such as the digital elevation model （DEM）， meteorological data， and power/signal coverage. A multi-criteria decision analysis （MCDA） method evaluates and scores candidates based on rigid and flexible criteria， including topographical suitability， wind speed， and power supply availability. A multi-objective optimization model is then developed to optimize the layout of hangars， incorporating critical constraints such as topographical characteristics， UAV power limits， and coverage redundancy. To solve this optimization problem， the non-dominated sorting genetic algorithm Ⅱ （NSGA-Ⅱ） is applied. Experimental results demonstrate that the proposed method outperforms traditional approaches， such as the greedy algorithm and the single-objective genetic algorithm. Specifically， the NSGA-Ⅱ method reduces the number of hangars by 8.3%， and increases the coverage by 1.6%. It also significantly accelerates the convergence， demonstrating superior performance and efficiency. This methodology provides a comprehensive solution for UAV deployment in forest inspections and can be adapted to other complex topography.
2026(3):386-399.
DOI: 10.16356/j.1005-1120.2026.03.005
Abstract:
With the rapid evolution of weapon systems towards precision and intelligence， unmanned aerial combat has increasingly transitioned from close-range engagements to beyond-visual-range （BVR） operations. This paper addresses the challenges of learning effective missile launch strategies in BVR air combat， where the long delay between weapon launch and target hit leads to sparse and delayed reward problems. This paper first extends the multi-agent proximal policy optimization （MAPPO） framework to incorporate expert rule-based launch control， resulting in MAPPO with launch constraints （MAPPO-LC）. This method ensures that missile launch decisions satisfy tactical constraints on distance， altitude and timing while providing the learning process with a viable starting policy. Building upon this baseline， this paper introduces MAPPO with reward return （MAPPO-RR）， a reward return mechanism that explicitly identifies missile launch and hit events as key decision nodes， and return the hit reward to the launch step. This reward redistribution method mitigates the delayed reward problem， and significantly accelerates policy convergence in multi-agent BVR scenarios. Experimental evaluation demonstrates that the MAPPO-RR algorithm achieves a win rate exceeding 75% and exhibits a sampling efficiency over 55% higher than that of the baseline method.
With the rapid evolution of weapon systems towards precision and intelligence， unmanned aerial combat has increasingly transitioned from close-range engagements to beyond-visual-range （BVR） operations. This paper addresses the challenges of learning effective missile launch strategies in BVR air combat， where the long delay between weapon launch and target hit leads to sparse and delayed reward problems. This paper first extends the multi-agent proximal policy optimization （MAPPO） framework to incorporate expert rule-based launch control， resulting in MAPPO with launch constraints （MAPPO-LC）. This method ensures that missile launch decisions satisfy tactical constraints on distance， altitude and timing while providing the learning process with a viable starting policy. Building upon this baseline， this paper introduces MAPPO with reward return （MAPPO-RR）， a reward return mechanism that explicitly identifies missile launch and hit events as key decision nodes， and return the hit reward to the launch step. This reward redistribution method mitigates the delayed reward problem， and significantly accelerates policy convergence in multi-agent BVR scenarios. Experimental evaluation demonstrates that the MAPPO-RR algorithm achieves a win rate exceeding 75% and exhibits a sampling efficiency over 55% higher than that of the baseline method.
XU Song
,
JI Guipeng
,
ZHAO Hongsheng
,
YU Tengli
,
WANG Ershen
,
QU Pingping
,
CHEN Yunhao
,
ZHANG Hongxuan
2026(3):400-411.
DOI: 10.16356/j.1005-1120.2026.03.006
Abstract:
Visible light cameras are excellent at capturing subtle features of moving targets in well-wit and stable scenes. However， such cameras may not be able to accurately detect targets when encountering occlusion， fluctuating light intensity， or shadow effects， leading to the occurrence of missed or false alarms. Aiming at the problem of poor anti-interference ability of visible light images in complex scenes， a target detection method based on the combination of visible light and infrared images is proposed. The Canny algorithm is used to preprocess the unmanned aerial vehicle （UAV） infrared image， the seed points are obtained through the Sobel operator， and the image segmentation is performed using the maximum inter-class variance value of the image as the growth criterion in order to locate the UAV region in the infrared image. Then the corresponding region of the visible image is cropped， and UAV target detection is performed in this region. The joint detection method narrows the scope of detection and effectively reduces the interference of factors such as illumination changes and interfering objects on the detection results. Experimental results show that the proposed method achieves 87.6% precision and 75.9% recall， with mAP0.5 and mAP0.5：0.95 values of 83.9% and 52.9%， respectively.
Visible light cameras are excellent at capturing subtle features of moving targets in well-wit and stable scenes. However， such cameras may not be able to accurately detect targets when encountering occlusion， fluctuating light intensity， or shadow effects， leading to the occurrence of missed or false alarms. Aiming at the problem of poor anti-interference ability of visible light images in complex scenes， a target detection method based on the combination of visible light and infrared images is proposed. The Canny algorithm is used to preprocess the unmanned aerial vehicle （UAV） infrared image， the seed points are obtained through the Sobel operator， and the image segmentation is performed using the maximum inter-class variance value of the image as the growth criterion in order to locate the UAV region in the infrared image. Then the corresponding region of the visible image is cropped， and UAV target detection is performed in this region. The joint detection method narrows the scope of detection and effectively reduces the interference of factors such as illumination changes and interfering objects on the detection results. Experimental results show that the proposed method achieves 87.6% precision and 75.9% recall， with mAP0.5 and mAP0.5：0.95 values of 83.9% and 52.9%， respectively.
2026(3):412-426.
DOI: 10.16356/j.1005-1120.2026.03.007
Abstract:
As a critical component of the turbine rotor， the baffle plays an essential role in ensuring safe and reliable operation of the aero-engine. This study addresses the issue of excessive local stress in the baffle of a high-pressure turbine disc. The structural design optimization is performed using the self-developed Zhizhou software integrated with the slime mould algorithm （SMA）. Leveraging advanced algorithms and comprehensive simulation interfaces， the Zhizhou software effectively exploits the potential of structural design， leading to significant improvements in structural performance. The SMA algorithm employs a positive feedback mechanism and adaptive strategies through the incorporation of fitness weights and oscillation factors. These parameters simulate the oscillatory contraction behavior of slime moulds， allowing the algorithm to dynamically adjust search direction and speed， thereby achieving an effective balance between local exploration and global optimization. During the optimization process， a sector sub-model is established， and the contact model is simplified using a force load equivalence approach to improve computational efficiency. Subsequently， a parametric model of the baffle is developed based on geometric characteristics， stress responses， and boundary constraints， with the variation ranges of key parameters being determined. A mathematical model is then formulated with the objective of minimizing the maximum equivalent stress， under the constraint of the axial support reaction force at the contact surface. Finally， an integrated design optimization workflow is constructed using Zhizhou in combination with Unigraphics （UG） and Workbenchs， as well as incorporating the SMA algorithm to optimize the baffle structure. After optimization， the maximum equivalent stress is decreased from 1 382.4 to 1 235.4 MPa， a reduction of 10.6%. Meanwhile， the axial support reaction force is increased from 4 158.9 to 4 330.6 N， a variation of 4.0%， which satisfies the requirement for being within 12%. These results validate the effectiveness of the SMA algorithm in the structural design optimization of the baffle and demonstrate the practical value of the Zhizhou software in engineering applications.
As a critical component of the turbine rotor， the baffle plays an essential role in ensuring safe and reliable operation of the aero-engine. This study addresses the issue of excessive local stress in the baffle of a high-pressure turbine disc. The structural design optimization is performed using the self-developed Zhizhou software integrated with the slime mould algorithm （SMA）. Leveraging advanced algorithms and comprehensive simulation interfaces， the Zhizhou software effectively exploits the potential of structural design， leading to significant improvements in structural performance. The SMA algorithm employs a positive feedback mechanism and adaptive strategies through the incorporation of fitness weights and oscillation factors. These parameters simulate the oscillatory contraction behavior of slime moulds， allowing the algorithm to dynamically adjust search direction and speed， thereby achieving an effective balance between local exploration and global optimization. During the optimization process， a sector sub-model is established， and the contact model is simplified using a force load equivalence approach to improve computational efficiency. Subsequently， a parametric model of the baffle is developed based on geometric characteristics， stress responses， and boundary constraints， with the variation ranges of key parameters being determined. A mathematical model is then formulated with the objective of minimizing the maximum equivalent stress， under the constraint of the axial support reaction force at the contact surface. Finally， an integrated design optimization workflow is constructed using Zhizhou in combination with Unigraphics （UG） and Workbenchs， as well as incorporating the SMA algorithm to optimize the baffle structure. After optimization， the maximum equivalent stress is decreased from 1 382.4 to 1 235.4 MPa， a reduction of 10.6%. Meanwhile， the axial support reaction force is increased from 4 158.9 to 4 330.6 N， a variation of 4.0%， which satisfies the requirement for being within 12%. These results validate the effectiveness of the SMA algorithm in the structural design optimization of the baffle and demonstrate the practical value of the Zhizhou software in engineering applications.
2026(3):427-442.
DOI: 10.16356/j.1005-1120.2026.03.008
Abstract:
Generative design methods have been widely applied in modern aircraft aerodynamic design. However， the integrated optimization of aerodynamic and stealth performance in aircraft still relies on surrogate models and multi-objective optimization algorithms. To address the complex verification and optimization procedures in current integrated aerodynamic-stealth aircraft design， this paper proposes a rapid generative design method based on a conditional denoising diffusion probability model （CDDPM）. First， the class-shape transformation （CST） method is employed for parametric modeling of airfoils. To build the aerodynamic and stealth performance datasets， the vortex lattice method and the physical optics method for large-sized objects are used to compute the lift-to-drag ratio （L/D） and radar cross-section （RCS）， respectively. Based on the dataset， a generative conditional diffusion model is implemented to achieve the mapping relationship from target performance （L/D and RCS） to CST parameters of wing airfoils. Validation results indicate that the prediction errors for the generative model in aerodynamic-stealth performance are smaller than 6%. Meanwhile， the generated airfoils exhibit notable diversity. Furthermore， optimization design of airfoils considering both aerodynamic and stealth performance is conducted， where the diffusion model is utilized to generate new airfoils to expand the design space. The pareto front is obviously expanded with the minimum RCS decreased by 28.6%， and the maximum L/D increased by 7.5%. This study establishes a generative model-based framework for rapid aerodynamic-stealth optimization of airfoils， laying a foundation for AI-driven multidisciplinary design optimization （MDO） in aircraft design.
Generative design methods have been widely applied in modern aircraft aerodynamic design. However， the integrated optimization of aerodynamic and stealth performance in aircraft still relies on surrogate models and multi-objective optimization algorithms. To address the complex verification and optimization procedures in current integrated aerodynamic-stealth aircraft design， this paper proposes a rapid generative design method based on a conditional denoising diffusion probability model （CDDPM）. First， the class-shape transformation （CST） method is employed for parametric modeling of airfoils. To build the aerodynamic and stealth performance datasets， the vortex lattice method and the physical optics method for large-sized objects are used to compute the lift-to-drag ratio （L/D） and radar cross-section （RCS）， respectively. Based on the dataset， a generative conditional diffusion model is implemented to achieve the mapping relationship from target performance （L/D and RCS） to CST parameters of wing airfoils. Validation results indicate that the prediction errors for the generative model in aerodynamic-stealth performance are smaller than 6%. Meanwhile， the generated airfoils exhibit notable diversity. Furthermore， optimization design of airfoils considering both aerodynamic and stealth performance is conducted， where the diffusion model is utilized to generate new airfoils to expand the design space. The pareto front is obviously expanded with the minimum RCS decreased by 28.6%， and the maximum L/D increased by 7.5%. This study establishes a generative model-based framework for rapid aerodynamic-stealth optimization of airfoils， laying a foundation for AI-driven multidisciplinary design optimization （MDO） in aircraft design.
2026(3):443-462.
DOI: 10.16356/j.1005-1120.2026.03.009
Abstract:
Accurate excitation current prediction is crucial for the high-performance control of synchronous machines （SMs）， which are widely employed in industrial drives such as electro-spindles. However， achieving accurate and generalizable prediction across multiple operating points is challenging due to coupled nonlinearities like thermal drift and magnetic saturation. This study proposes a novel prediction model based on the extended long short-term memory （xLSTM） network. The model integrates scalar LSTM （sLSTM） and matrix LSTM （mLSTM） units and leverages an exponential gating mechanism to enhance the capability for learning complex nonlinear mappings and long-term dependencies. Specifically， the vectorized parallel memory structure of sLSTM is suited to capturing slow parameter variations caused by thermal drift， while the matrix associative memory mechanism of mLSTM excels at learning multi-variable nonlinear coupling effects such as magnetic saturation. These two modules form a complementary hybrid architecture. Comparative analyses against traditional LSTM and gate recurrent unit （GRU） benchmarks were conducted using SM monitoring data covering various load and excitation conditions. In addition， an ablation study was performed using xLSTM with varying blending ratios of scalar and matrix LSTM components. Evaluation based on multiple error metrics and computational time demonstrates that the proposed xLSTM achieves superior accuracy， stronger generalization， lower computational overhead， and higher prediction stability. The underlying mechanisms are analyzed from architectural and algorithmic perspectives. These findings offer a novel data-driven modeling approach for SM excitation current， with potential value for applications requiring high-fidelity motor state estimation.
Accurate excitation current prediction is crucial for the high-performance control of synchronous machines （SMs）， which are widely employed in industrial drives such as electro-spindles. However， achieving accurate and generalizable prediction across multiple operating points is challenging due to coupled nonlinearities like thermal drift and magnetic saturation. This study proposes a novel prediction model based on the extended long short-term memory （xLSTM） network. The model integrates scalar LSTM （sLSTM） and matrix LSTM （mLSTM） units and leverages an exponential gating mechanism to enhance the capability for learning complex nonlinear mappings and long-term dependencies. Specifically， the vectorized parallel memory structure of sLSTM is suited to capturing slow parameter variations caused by thermal drift， while the matrix associative memory mechanism of mLSTM excels at learning multi-variable nonlinear coupling effects such as magnetic saturation. These two modules form a complementary hybrid architecture. Comparative analyses against traditional LSTM and gate recurrent unit （GRU） benchmarks were conducted using SM monitoring data covering various load and excitation conditions. In addition， an ablation study was performed using xLSTM with varying blending ratios of scalar and matrix LSTM components. Evaluation based on multiple error metrics and computational time demonstrates that the proposed xLSTM achieves superior accuracy， stronger generalization， lower computational overhead， and higher prediction stability. The underlying mechanisms are analyzed from architectural and algorithmic perspectives. These findings offer a novel data-driven modeling approach for SM excitation current， with potential value for applications requiring high-fidelity motor state estimation.
2026(3):463-474.
DOI: 10.16356/j.1005-1120.2026.03.010
Abstract:
Machine learning provides a fast and accurate tool for the prediction of a physical model. In this paper， a machine learning framework based on the physics-informed neural network （PINN） was established to predict the linear elastic static deformation of plate and shell structures. In contrast to the purely data-driven neural network， PINN incorporates the physical laws into the training process， thus reducing the required amount of data. The loss functions of the PINN are constructed based on the total potential energy functions of the thin-walled structure. Besides， the proposed PINN can be easily extended to shell structures with multiple patches by adding interface compatibility constraints into the loss function. The performance of the PINNs with the energy-based loss functions was evaluated with different shell structures and compared with the finite element results. Numerical examples show that the highly accurate results can be achieved based on the proposed framework which significantly reduces the amount of required training data compared to the data-driven neural network.
Machine learning provides a fast and accurate tool for the prediction of a physical model. In this paper， a machine learning framework based on the physics-informed neural network （PINN） was established to predict the linear elastic static deformation of plate and shell structures. In contrast to the purely data-driven neural network， PINN incorporates the physical laws into the training process， thus reducing the required amount of data. The loss functions of the PINN are constructed based on the total potential energy functions of the thin-walled structure. Besides， the proposed PINN can be easily extended to shell structures with multiple patches by adding interface compatibility constraints into the loss function. The performance of the PINNs with the energy-based loss functions was evaluated with different shell structures and compared with the finite element results. Numerical examples show that the highly accurate results can be achieved based on the proposed framework which significantly reduces the amount of required training data compared to the data-driven neural network.
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