Element-wise physics-informed neural network approach for 2D linear elasticity problems
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https://doi.org/10.15625/0866-7136/23782Keywords:
physics informed neural network, deep neural network, total potential energy, plane stress, plane strainAbstract
Physics-Informed Neural Networks (PINNs) have emerged as a promising framework for solving solid mechanics problems. Most existing PINN frameworks approximate continuous displacement fields and are trained using collocation points. However, several challenges remain when addressing problems involving complex geometries, concentrated forces, and material heterogeneity. This study proposes an Element-Wise Physics-Informed Neural Network (EWPINN) framework for two-dimensional linear elasticity, in which the Neural Network (NN) operates directly on the discrete nodal degrees of freedom defined on a predefined finite element mesh. The structural response is obtained by minimizing the total potential energy, evaluated element-wise over a triangular mesh, thereby eliminating the need for collocation points and derivative-based loss terms. As a result, the proposed model requires significantly fewer training data points and exhibits improved training efficiency compared to conventional PINN approaches. By operating on a mesh-based formulation, the EWPINN can effectively handle complex geometries, concentrated forces, and piecewise heterogeneous materials. The effectiveness and robustness of the proposed approach are demonstrated through several numerical examples. The obtained structural responses exhibit excellent agreement with reference FEM solutions. The proposed framework provides a differentiable energy-based alternative that can be readily integrated into optimization pipelines and extended to nonlinear problems.
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