By combining time-varying mechanics and damage theory, basic equations and numerical equations of visco-elastic-plastic time-varying damage mechanics are given.

By combing time-varying mechanics and damage theory, variable damage parameter which correlated with variational course is introduced.

It was discussed that time-variation mechanics applied in civil engineering, such as in materials, structural analysis, foundation engineering, and construction.

But its development and systematization need the clear understand of its foundation──time-variation mechanics.

A new problem of solid mechanics for time-variation mechanics analyses is presented in this paPer, in which its basic tasks, characters aJs well as mechanical and mathematical methods are given, the importance and development are demonstrated by some engineering examples.

Based on the established rock damage model and theory of time variation mechanics, the stress and strain calculation is processed according to the different path of excavation in this paper.

In this paper, the stability of construction for the bridge is studied by the method of time variation mechanics, and it describes well the structural behavior during construction.

By using Lagrange equations based on time-vary dynamics, the systematic equations on vehicle-bridge coupled vibratoin were formulated.

The principle variation of beam deflection is calculated with two variable parameters: the initial speed and the acceleration of moving mass, using the solution method of time-variant mechanical system.