Mesh reduction methods for thermoelasticity of laminated composite structures: Study on the B-spline based State Space Finite Element Method and Physics-Informed Neural Networks

Abstract

Calculating the mechanical characteristics such as interlaminar stresses of composite laminated structures is a major challenge. To avoid the disadvantages of the traditional finite element method (FEM) of discretizing the whole structure too cumbersome, we implemented a method which only need to discretize on horizontal planes. The state space differential equation is derived from the Hellinger–Reissner variational principle, and both quadratic and cubic B-splines are used to interpolate the in-plane physical quantities, while the precise integration method is carried out along thickness to obtain accurate numerical results efficiently. The method is hence treated as the B-spline based State Space FEM (B-SSFE). To further reduce degree of freedoms, we implemented another method based on physics-informed neural networks (PINNs), which is completely meshless. Deep Learning is combined with differential equations carrying physical information, and neural networks are trained by constraining the loss function. We calculated different boundary conditions for a 3D composite laminated plate under thermal loading. Comparison is conduct among B-SSFE, PINNs and FEM. Numerical results demonstrate that in terms of computational accuracy, B-SSFE can be more accurate than FEM dealing with complex boundary conditions, and PINNs can reflects the stress fields well.