Variational Theory For Coupling And Numerical Computing In Rolling Process

Temperature is an important factor of influence metal's deformation and material's per-formance in rolling process, moreover, it often goes with temperature's transformation when the metal is happening deformation. In addition, the plastic work also translate into hot, there-fore, it is very necessary to structure coupled equations of temperature and deformation and it is also very necessary to carry through integrative simulation computing in order to improve the precision of numerical computing in rolling process. Variational theory plays a significant action in Finite element theory and Finite element simulation computing of the thermo-mechanical coupling of flat hot rolling process with the aid of rigid-plastic FEM model in the paper. Following are the main contents:(1) Coupled theory for velocity field and temperature field of workpiece. Equation of heat conduction is regarded as constraint condition, and pulled into the Lagrange multiplier, and structured the new Lagrangian functional in rolling process. The variational theories are applied to structure the couple of deformation and temperature.(2) Structuring the coupled equations. By doing variational method and discrete method, the coupled equations are structured. By solving the coupled equations, the Corresponding program of temperature field and deformation field is compiled, and the computing precision of coupling is validated by using the on-site data.(3) Solving methods of liner equations are discussed. In the progress of Newton iteration method for numerical calculation, Hessian matrix is usually to deal with, and the Hessian matrix of the coupled equations is symmetrical. LU decompounding method of the part selection of main element and modified Cholesky factorization forcing matrix to be positive definite method are adopted to solve good-sized zonal symmetrical linear equations. Comparing and analyzing of the result of the solution of LU decompounding method and modified Cholesky factorization forcing matrix to be positive definite, so the rationality of the coupling theory is to be validated, and the advantage of the numerical algorithms is also to be proved.