Physics-Informed Neural Networks (PINNs) have gained considerable interest in diverse engineering domains thanks to their capacity to integrate physical laws into deep learning models. Recently, geometry-aware PINN-based approaches that employ the strong form of underlying physical system equations have been developed with the aim of integrating geometric information into PINNs. Despite ongoing research, the assessment of PINNs in problems with various geometries remains an active area of investigation. In this work, we introduce a novel physics-informed framework named the Geometry-Aware Deep Energy Method (GADEM) for solving structural mechanics problems on different geometries. As the weak form of the physical system equation (or the energy-based approach) has demonstrated clear advantages compared to the strong form for solving solid mechanics problems, GADEM employs the weak form and aims to infer the solution on multiple shapes of geometries. Integrating a geometry-aware framework into an energy-based method results in an effective physics-informed deep learning model in terms of accuracy and computational cost. Different ways to represent the geometric information and to encode the geometric latent vectors are investigated in this work. We introduce a loss function of GADEM which is minimized based on the potential energy of all considered geometries. An adaptive learning method is also employed for the sampling of collocation points to enhance the performance of GADEM. We present some applications of GADEM to solve solid mechanics problems, including a loading simulation of a toy tire involving contact mechanics and large deformation hyperelasticity. The numerical results of this work demonstrate the remarkable capability of GADEM to infer the solution on various and new shapes of geometries using only one trained model.

Attempt to use convolutional neural network to achieve kinematic analysis of plane bar structure. Through 3dsMax animation software and OpenCV module, self-build image dataset of geometrically stable system and geometrically unstable system. we construct and train convolutional neural network model based on the TensorFlow and Keras deep learning platform framework. The model achieves 100% accuracy on the training set, validation set, and test set. The accuracy on the additional test set is 93.7%, indicating that convolutional neural network can learn and master the relevant knowledge of kinematic analysis of structural mechanics. In the future, the generalization ability of the model can be improved through the diversity of dataset, which has the potential to surpass human experts for complex structures. Convolutional neural network has certain practical value in the field of kinematic analysis of structural mechanics. Using visualization technology, we reveal how convolutional neural network learns and recognizes structural features. Using pre-trained VGG16 model for feature extraction and fine-tuning, we found that the generalization ability is inferior to the self-built model.