An improved plate deep energy method for the bending, buckling and free vibration problems of irregular Kirchhoff plates

Abstract

An improved plate deep energy method without penalty terms is introduced to study the bending, free vibration and buckling problems of irregular Kirchhoff plates. The finite difference produced by convolution operation is employed for a faster calculation of derivatives and enforcement of boundary conditions. Most deep learning based neural network methods adopt the penalty method to impose boundary constraints, which may cause convergence issues especially when dealing with complex solution domain or mixed boundary conditions. In this paper, the R-function is utilized to build the distance function multiplied by the neural network output to meet the Dirichlet boundary constraints, while the boundary constraints expressed by derivative functions are applied by introducing virtual nodes. With such treatments, the boundary losses of a plate system can be avoided. To validate the proposed method, numerical examples considering plates with irregular shapes and mixed boundary conditions are studied, and the results are compared to those provided by the theoretical solutions, finite element method (FEM), and literature.