A robust physics-informed neural network approach for predicting structural instability

In this work, a direct physics-informed neural network (DPINN) is first proposed to analyze the stability of truss structures that incremental-iterative algorithm is completely removed from the implementation process. Instead of resolving of nonlinear equations as in conventional numerical methods, a neural network (NN) is employed to minimize the loss function which is designed to guide the training network based on the structural instability information. In our computational framework, the parameters including weights and biases of the network are considered as design variables. In addition, spatial coordinates of joints are examined as input data, while corresponding displacements and load factor unknown to the network are taken account of output. To address this challenge, the predicted outputs obtained by feedforward are utilized to establish the loss function relied on the residual load and stiffness characteristics of the structure as the first stage. And then, back-propagation and optimizer are applied to automatically calculate sensitivity and adjust parameters of the network, respectively. This entire process known as training is repeated until convergence. To that end, the position of the critical point is indicated as soon as the training ends by our network without using any time-consuming incremental-iterative algorithms as well as structural analyses. Several benchmark examples of truss structures associated with the geometric nonlinearity influence are investigated to evaluate the efficiency of the proposed scheme. The obtained results reveal that the present framework is extremely simple to implement and also yields the strong robustness as well as higher accuracy.

Automated summary

In this study, a direct physics-informed neural network (DPINN) is proposed to analyze the stability of truss structures without the use of incremental-iterative algorithms. A neural network is used to minimize a loss function based on structural instability information. The network parameters are considered as design variables, and joint coordinates are used as input while displacements and load factors are output. The training process involves predicting outputs, establishing a loss function, and using back-propagation and optimization to adjust network parameters until convergence is achieved. The proposed scheme is shown to be efficient and accurate in evaluating the stability of truss structures with geometric nonlinearity.