Research on static and dynamic mechanical response of mechanical structures based on theoretical mechanics methods

Abstract

This study introduces a novel computational method for the fast computation of static and dynamic mechanical response and optimization of parameters of mechanical structures. A prediction optimisation model of static and dynamic response is proposed, combining theoretical mechanics, finite element simulation and neural network. A simulation data set is created based on the modelling of stiffness, mass and damping matrices. The stress, displacement, modal frequencies and vibration risk are collaboratively analysed by using multi-layer neural networks, CNN-LSTM, and particle swarm optimisation algorithms. Experimental results indicate that the model’s maximum stress RMSE is 5.18MPa, outperforming the response surface method’s 11.84 MPa; the displacement RMSE is 0.041 mm, with an R² of0.974. Following optimisation, the maximum equivalent stress decreased by 14.85% and the first-order natural frequency increased by 14.79%, validating the effectiveness of the method.