The accurate mechanical analysis of thick-walled pressure vessel structures composed of advanced materials,such as hyperelastic and functionally graded materials(FGMs),is critical for ensuring their safety and optimiz...The accurate mechanical analysis of thick-walled pressure vessel structures composed of advanced materials,such as hyperelastic and functionally graded materials(FGMs),is critical for ensuring their safety and optimizing their design.However,conventional numerical methods can face challenges with the non-linearities inherent in hyperelasticity and the complex spatial variations in FGMs.This paper presents a novel hybrid numerical approach combining Physics-Informed Neural Networks(PINNs)with Finite Element Method(FEM)derived data for the robust analysis of thick-walled,axisymmetric,heterogeneous,hyperelastic pressure vessels with elliptical geometries.A PINN framework incorporating neo-Hookean constitutive relations is developed in MATLAB.To enhance training efficiency and accuracy,the PINN’s loss function is augmented with displacement data obtained from high-fidelity FEM simulations performed in ANSYS.The methodology is rigorously validated by comparing PINN-predicted displacement and von Mises stress fields against ANSYS benchmarks for various scenarios of FGMconfigurations(with material properties varying according to a power law)subjected to internal and external pressurization.The results demonstrate excellent agreement between the proposed hybrid PINN-FEMapproach and conventional FEMsolutions across all test cases,accurately capturing complex deformation patterns and stress concentrations.This study highlights the potential of data-augmented PINNs as an effective and accurate computational tool for tackling complex solid mechanics problems involving non-linearmaterials and significant heterogeneity,offering a promising avenue for future research in engineering design and analysis.展开更多
In this paper,the physics informed neural network(PINN)deep learning method is applied to solve two-dimensional nonlocal equations,including the partial reverse space y-nonlocal Mel'nikov equation,the partial reve...In this paper,the physics informed neural network(PINN)deep learning method is applied to solve two-dimensional nonlocal equations,including the partial reverse space y-nonlocal Mel'nikov equation,the partial reverse space-time nonlocal Mel'nikov equation and the nonlocal twodimensional nonlinear Schr?dinger(NLS)equation.By the PINN method,we successfully derive a data-driven two soliton solution,lump solution and rogue wave solution.Numerical simulation results indicate that the error range between the data-driven solution and the exact solution is relatively small,which verifies the effectiveness of the PINN deep learning method for solving high dimensional nonlocal equations.Moreover,the parameter discovery of the partial reverse space-time nonlocal Mel'nikov equation is analysed in terms of its soliton solution for the first time.展开更多
本文采用物理信息神经网络(PINN)来求解不可压缩湍流Navier-Stokes方程。本研究引入了动态权重调整策略,使得各项误差在训练过程中得到适当的平衡,从而避免了某些误差项主导整个训练过程的问题。此外,为了加速训练收敛并提高精度,本研...本文采用物理信息神经网络(PINN)来求解不可压缩湍流Navier-Stokes方程。本研究引入了动态权重调整策略,使得各项误差在训练过程中得到适当的平衡,从而避免了某些误差项主导整个训练过程的问题。此外,为了加速训练收敛并提高精度,本研究还对网络结构进行了优化,结合物理约束优化过程,改变了优化方法,提高了模型的训练效率。In this paper, physical information neural networks (PINN) are used to solve the Navier-Stokes equations of incompressible turbulence. In this study, the dynamic weighting adjustment strategy is presented to make the errors properly balanced in the training process, so as to avoid the problem that some error terms dominate the whole training process. In addition, in order to accelerate the training convergence and improve the accuracy, this study also optimized the network structure, combining with the physical constraint optimization process and changing the optimization method to improve the training efficiency of the model.展开更多
文摘The accurate mechanical analysis of thick-walled pressure vessel structures composed of advanced materials,such as hyperelastic and functionally graded materials(FGMs),is critical for ensuring their safety and optimizing their design.However,conventional numerical methods can face challenges with the non-linearities inherent in hyperelasticity and the complex spatial variations in FGMs.This paper presents a novel hybrid numerical approach combining Physics-Informed Neural Networks(PINNs)with Finite Element Method(FEM)derived data for the robust analysis of thick-walled,axisymmetric,heterogeneous,hyperelastic pressure vessels with elliptical geometries.A PINN framework incorporating neo-Hookean constitutive relations is developed in MATLAB.To enhance training efficiency and accuracy,the PINN’s loss function is augmented with displacement data obtained from high-fidelity FEM simulations performed in ANSYS.The methodology is rigorously validated by comparing PINN-predicted displacement and von Mises stress fields against ANSYS benchmarks for various scenarios of FGMconfigurations(with material properties varying according to a power law)subjected to internal and external pressurization.The results demonstrate excellent agreement between the proposed hybrid PINN-FEMapproach and conventional FEMsolutions across all test cases,accurately capturing complex deformation patterns and stress concentrations.This study highlights the potential of data-augmented PINNs as an effective and accurate computational tool for tackling complex solid mechanics problems involving non-linearmaterials and significant heterogeneity,offering a promising avenue for future research in engineering design and analysis.
文摘In this paper,the physics informed neural network(PINN)deep learning method is applied to solve two-dimensional nonlocal equations,including the partial reverse space y-nonlocal Mel'nikov equation,the partial reverse space-time nonlocal Mel'nikov equation and the nonlocal twodimensional nonlinear Schr?dinger(NLS)equation.By the PINN method,we successfully derive a data-driven two soliton solution,lump solution and rogue wave solution.Numerical simulation results indicate that the error range between the data-driven solution and the exact solution is relatively small,which verifies the effectiveness of the PINN deep learning method for solving high dimensional nonlocal equations.Moreover,the parameter discovery of the partial reverse space-time nonlocal Mel'nikov equation is analysed in terms of its soliton solution for the first time.
文摘本文采用物理信息神经网络(PINN)来求解不可压缩湍流Navier-Stokes方程。本研究引入了动态权重调整策略,使得各项误差在训练过程中得到适当的平衡,从而避免了某些误差项主导整个训练过程的问题。此外,为了加速训练收敛并提高精度,本研究还对网络结构进行了优化,结合物理约束优化过程,改变了优化方法,提高了模型的训练效率。In this paper, physical information neural networks (PINN) are used to solve the Navier-Stokes equations of incompressible turbulence. In this study, the dynamic weighting adjustment strategy is presented to make the errors properly balanced in the training process, so as to avoid the problem that some error terms dominate the whole training process. In addition, in order to accelerate the training convergence and improve the accuracy, this study also optimized the network structure, combining with the physical constraint optimization process and changing the optimization method to improve the training efficiency of the model.
