关键词: 鼓肚变形, 连铸板坯, 黏弹性板坯, 辛几何法

Abstract: For the bulging deformation of the slab shell in slab continuous casting machine, the viscoelastic behaviors of the slab shell under high temperature and its coupling characteristics of elastic deformation and viscous deformation are considered, and a model of viscoelastic rectangular plate with four clamped edges for the bulging deformation of the slab shell is presented. Based on the Laplace’s transform and elastic-viscoelastic corresponding principle, the partial differential equation of four order of viscoelastic plate in the Laplace domain is derived, and then transferred into Hamilton canonical equation in the Laplace domain. For whole state variables, using the separation of variables, eigenfunction expansion in the symplectic geometry, conjugate symplectic orthogonal normalized relations and Laplace’s inverse transform, the analytical solution of the deflection for the viscoelastic slab with four edges clamped is obtained in time domain. Taking a slab continuous casting machine as an examples, the effect of elastic deformation, creep deformation and relaxation time of the material on the bulging deformation are analyzed, and the bending moment per unit length of the middle point for the solidified shell versus time are given.

Key words: bulging deformation, continuous casting slab, symplectic geometric method, viscoelastic slab