a mesh-free physics-informed neural network framework for solving plane problems without locking issues

This study proposes a plane problem solving method based on physics-informed neural network (pinn) for dealing with plane stress and strain problems, effectively avoiding the common shear locking and volume locking phenomena in traditional finite element methods, and exploring their underlying mechanisms. for the problem of plane stress, a pinn model based on strong form partial differential equations was constructed by randomly generating interior and boundary points within the solution domain, embedding the stress equilibrium equations and constitutive relations into the loss function. by minimizing the loss function, the network can automatically learn stress and displacement fields that satisfy the governing equations and boundary conditions. numerical experiments show that this method can accurately predict stress distribution, effectively avoid shear locking, and maintain high accuracy even in thin plate structures. further extension of the method to plane strain problems also successfully solved volume locking. this study also systematically compares two loss function construction methods based on strong form and energy principle (weak form). the results show that pinn, with its continuous and meshless solving characteristics, can fundamentally avoid the locking problem caused by low order element discretization, and both forms have high accuracy. this study validates the effectiveness and superiority of pinn in planar problems, providing new ideas and theoretical basis for overcoming traditional finite element locking problems. this method does not require complex element construction or numerical integration, and combines computational efficiency and accuracy, with good engineering application prospects.