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

What is it about?

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.

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Photo by Ricardo Gomez Angel on Unsplash

Photo by Ricardo Gomez Angel on Unsplash