Numerical Simulation On Solidification And Thermal Stress Of Solid Shell In Continuous Casting Mold Based On Meshless Method

Meshless method is a new technique for the numerical analysis. The objective of this thesis is to investigate its usability for calculating the solidification and thermal stress of solid shell in continuous casting mold. Two types of collocation meshless methods, i.e. the Radial Base Functions Method (RBFM) and the Finite Point Method (FPM), are preliminarily studied for the application in the analysis of heat transfer and solidification problem. Based on Gauss-Seidel iteration and relaxation iteration, two iterative schemes are constructed and examined for the meshless computation after analyzing the solution equilibrium equations of RBFM. Both iteration schemes are free of assembling the interpolation matrix and are advantageous for solving large-scale engineering problems with a reasonable storage space. Numerical analysis shows that the FPM is flexible in the practical application. For FPM, the amplification coefficient of support domain radius of weight function, ac, with a high accuracy in solving 2-D problems, also performs a good ability in the analysis of similar problems. These observations provide a foundation for the analysis of solidification and thermal stress of solid shell in continuous casting mold by the meshless method. The meshless scheme for the solidification analysis is developed based on FPM, and the nonlinear characteristics of the material properties and solidification enthalpy are treated. The Neumann boundary conditions are constructed based on Onate stabilization method and the solution accuracy is increased. The meshless scheme is verified by solving the classical solidification problems. In sequence, a meshless scheme for solving the elasto-plastic thermal stress is built based on Local Petrov-Galerkin Method (MLPG). According to the incremental tangent-stiffness methods used in the finite element method, a similar meshless scheme is constructed for solving thermal elasto-plastic material problem. The thermal stress analysis scheme is verified with the patch test, simple tension and isothermal expansion problems. Finally, a meshless software package for the simulation of solidification and thermal stress of solid shell in the continuous casting mold is developed. The calculation results for a billet show that non-uniform temperature distribution of solid shell may lead a plastic strain concentration and a deformation at off-corner region in billet. The air gap, which occurs at the billet corner, reduces the surface heat flux, so the shell thickness becomes thin. Furthermore, the expansion of air gap will aggravate the temperature non-uniformly in the billet crosses section, and the large stress and strain may happen at the billet off-corner. Moreover it is applied to analyze the solid shell growth of a continuous casting large square bland in mold, and the results show that the computation solution is coincided with the measurement. The research shows that meshless method can be used to analyze the solidification and thermal stress of solid shell in continuous casting mold, and the calculation results is consistent with the characteristic of stress and strain distribution and the formation mechanism of the off-corner defects in continuous casting billet. It also indicates that the meshless method can obtain a similar calculation precision as FEM. These observations show that meshless method is a potent numerical analysis tool, and it is worth for the analysis of the continuous casting process.