DEFLECTION-BENDING MOMENT COUPLING NEURAL NETWORK METHOD FOR THE BENDING PROBLEM OF THIN PLATES WITH IN-PLANE STIFFNESS GRADIENT

A neural network method is developed to solve the bending problems of functionally graded thin plates with in-plane stiffness gradient in this paper. The partial differential equation (PDE) of the bending of thin plates with in-plane stiffness gradient is a complex fourth-order PDE. The conventional neural network solution based on strong form, may face the problem of slow convergence and the boundary conditions are difficult to handle when solving the PDE. According to the Kirchhoff thin plate bending theory, a neural network solution to the bending problem of thin plates with any in-plane stiffness gradient in rectangular coordinate system is proposed in this paper. The neural network model includes deflection network and bending moment network, which are used to predict the deflection and bending moment of the thin plate respectively. Thus, the solution of the fourth-order PDE is transformed into a series of second-order PDEs. By constructing trial function of the deflection and bending moment, the results of neural network calculation can be strictly satisfied the boundary conditions. In the back propagation process, training error is calculated according to the error function formula proposed in this paper and combining Adam optimization algorithm to update the internal parameters of the neural networks. In this paper, the bending problems of thin plate with in-plane stiffness gradient with different boundary conditions and shapes are solved, and the calculated results are compared with theoretical solutions or those of finite element solutions. It shows that the proposed method is suitable for solving the bending problem of thin plate with in-plane stiffness gradient. And the convergence of bending moment network is slower than the deflection network. However, it is robust and easier in dealing with boundary conditions.