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| Physics information neural network method for solving plane stress problems |
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Abstract This article proposes a method for solving plane stress problems based on Physical Information Neural Network (PINN). Firstly, inner and boundary particles are randomly generated in the solution domain [x, y]. Then, the geometric equations, constitutive equations, equilibrium equations, and boundary condition physical constraints of inner particles in the plane stress problem are introduced into the loss function of the neural network model, making the model physically meaningful. By minimizing the loss function, it approximates the solution of partial differential equations (PDEs). It can be seen that this method does not involve the process of grid partitioning, only the process of optimizing and training the loss functions of inner and boundary particles. Therefore, the PINN method is essentially a meshless method that can solve the shear locking problem caused by mesh partitioning in traditional finite element plane stress analysis. Subsequently, the feasibility and effectiveness of the proposed method were verified by comparing the finite element method (FEM) through numerical examples. The analysis of the calculation results shows that the PINN method can solve plane stress problems without the need for any label data, as well as solve the finite element defect of shear locking caused by false shear deformation in the finite element model due to mesh division.
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Received: 20 August 2024
Published: 23 April 2025
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2025, Vol. 46 
