On Springback Energy Principles of Finite Displacement Theory in Material Forming Processes

摘要

The conceptions of springback anti-coupled systems and equations for finite displacement theory are initially introduced. By the use of weighted residual method to the springback anti-coupled equations, the springback principles of minimum potential energy and stationary complementary energy of finite displacement theory are first established. On the basis of Lagrange multiplier method, the related generalized springback variational principles are then given. Next, springback principles of virtual work and virtual complementary work are directly derived from the above two springback variational principles. Meanwhile, springback reciprocal theorem and springback principle of deformation energy of finite displacement theory are set up by means of the springback anti-coupled equations. Finally, a numerical example is calculated by means of the springback principle of minimum potential energy of bending of the straight beams with large deflection.