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Most methods for solving plane stress problems currently rely on the finite element method (FEM), which is widely accepted for its established effectiveness in various engineering applications. However, FEM often suffers from shear locking during the solution process. To address this challenge and improve the solution of plane stress problems without the risk of shear locking, this paper adopts a physics-informed neural network (PINN) approach. The PINN framework integrates physical laws directly into the neural network training, allowing for the bypassing of traditional mesh requirements, which presents a considerable advantage. In this approach, internal and boundary points are randomly generated within the specified domain[x, y], serving as the basis for calculations. The geometric equations, constitutive equations, and balance equations that describe the behavior of the materials involved are incorporated into the model. Additionally, the physical constraints of boundary conditions for the boundary points are included in the loss function of the neural network model. This integration ensures that the model accurately reflects physical reality and adheres to the governing equations. By minimizing the loss function, the model effectively approximates the solution of the partial differential equations (PDEs) associated with plane stress problems. Importantly, this method does not require mesh generation, simplifying the computational process. Instead, it focuses solely on optimizing the loss functions for the internal and boundary points. To validate the proposed approach, further analysis is conducted to compare the PINN method with traditional FEM. The results demonstrate that the PINN method can solve plane stress problems without the need for labeled data. Furthermore, it effectively addresses finite element defects arising from spurious shear deformation due to mesh generation, specifically shear locking. Additionally, case studies indicate that the PINN method maintains high accuracy even with complex boundaries and varying stress conditions. This feature suggests that the method has significant potential for practical engineering applications in the future.
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| 科 Family | 属数 Number of genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) | 属 Genus | 种数 Number of species | 占总种数比例 Percentage of total species (%) |
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| 鹅膏菌科Amanitaceae | 2 | 11 | 5.26 | 鹅膏菌属 Amanita | 10 | 4.78 |
| 小菇科 Mycenaceae | 2 | 12 | 5.74 | 丝盖伞属 Inocybe | 5 | 2.39 |
| 多孔菌科 Polyporaceae | 8 | 14 | 6.70 | 蜡蘑属 Laccaria | 5 | 2.39 |
| 红菇科 Russulaceae | 3 | 23 | 11.00 | 小皮伞属 Marasmius | 6 | 2.87 |
| 小菇属 Mycena | 11 | 5.26 | ||||
| 光柄菇属 Pluteus | 5 | 2.39 | ||||
| 红菇属 Russula | 17 | 8.13 | ||||
| 栓菌属 Trametes | 5 | 2.39 |
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