SIMULATED VARIATIONAL PRINCIPLES AND GENERALIZED SIMULATED VARIATIONAL PRINCIPLES FOR SIMILARLY NO-COUPLED SYSTEM IN METAL FORMING TECHNOLOGY

The conceptions of similarly no-coupled system and equations are introduced in this paper. Simulated potential energy principle and simulated complementary energy principle for similarly no-coupled system in metal forming technology are established by applying weighted residual method to the similarly no-coupled equation. Generalized simulated potential energy principle and generalized simulated complements energy principle are derived from the simulated potential energy principle and the simulated complementary energy principle by Lagrange multiplier method. Applications of the simulated potential energy principle are given.These simulated variational principles have laid theoretical foundations for correctly transforming mechanics field quantities of the model into those of the prototype which observes geometrical simulidutes to the model, but has different boundary conditions and constitutive relations from those of the model.