The principle of total potential energy with stationary value in elastic system dynamics and the vibration analysis of train-bridge time-varying system;

Based on the total potential energy of elastic curved beams by considering the geometrical nonlinearity, the theoretic solution for the flexural-torsional buckling load of fixed-end circular arches subjected to uniform compression and bending is deduced with the Retz method, taking the effects of warping rigidity into account.

Based on the fundamental assumptions of thin walled structure,the geometrically nonlinear total potential energy was obtained by adopting an exact warping displacement of curved beam with biaxially symmetric cross section.

Annotation of total potential energy function for dynamic failure of rock;

As a main indicator of structural stability, the total potential energy equation for thin-walled members is widely referred to in academeic research and practical design of steel structures.

This paper discusses the inadequacies in Lagrange s equations and in Hamilton s principle and introduces the principle of total potential energy with stationary value in elastic system dynamics and the "Set in right position" rule for formulating matrixes, both were first presented by Zeng Qing yuan 22 years ago.