In this paper, we utilize Physics-Informed Neural Networks (PINNs) without any labeled data to solve the fourth-order partial differential equation governing
the bending of thin plates. We meticulously formulate and apply our framework to the
bending problem of elastic thin plates. Our findings indicate that defining each solution variable through an independent network, meaning without shared network parameters, yields superior performance compared to a single-network model with multiple outputs. During the training process, we discovered that more accurate results
were achieved by adjusting the network architecture to strictly satisfy the boundary
conditions, rather than incorporating them as part of the loss function. Remarkably,
the PINNs are capable of obtaining relatively good results without the use of any labeled data during training, irrespective of whether soft or hard constraints are applied.
In the end, the neural network’s predictions for plate deflection, stress, strain, bending,
and shear force all have errors less than 5% compared to the analytical solutions. In
the algorithm implementation phase, we leverage the Python library DeepXDE, which
facilitates the training of PINNs by providing an efficient and expedited process.
