The evolutions and inspirations of some research methods in mechanics

At different stages of development, appropriate methodologies can always be discovered or proposed in mechanics to address the critical issues faced at the time, which helps facilitate the development of mechanics itself. This paper analyzes the role and the evolution process of research methods in mechanics from four perspectives, respectively, geometric and analytical method, qualitative and quantitative analysis, simplified and precise model, differentiation and variational method. The development law of mechanics enlightens the essence of mechanics and provides inspirations for the scientific research and education under the assistance of artificial intelligence.