The Study And Application Of Parameters Element Of Finite Element Menthod Of Lines In Heat Conduction

Finite Element Method of Lines is a semi-discrete approach. It based on Kantorwicz method, which discrete in one direction and use analytical solutions in the other direction, so finally obtaining a set of ordinary differential equations instead of linear algebraic equations. Finite Element Method of Lines solve the problem ultimately attributable to solve ordinary differential equations under the boundary conditions with the help of ordinary differential equation solver. As COLSYS solver is easy to use, calculate fast and has good compatibility, so the program of the paper employs COLSYS solver.Finite Element Method of Lines is presented in the nineties of twentieth century. Initially it was applied in solid mechanics, With the development in twenty years, it has achieved good results. In recent years, in the context of fire resistance of steel structure, our group introduce Finite Element Method of Lines into Heat Transfer for the first time,through the analysis of the temperature field of steel structure under fire, which provide inspiration and basis for the fire resistant design of steel structures. After years of effort, our group has been developed a special program of Finite Element Method of Lines-TFEMOL for solving the steady-state temperature field and transient temperature field. The program TFEMOL mainly includes axisymmetric element and plane element.Axisymmetric element and plane element can only solve the temperature field of the regular geometry.In order to solve the irregular geometry of the temperature field, this paper presents parameters element of the Finite Element Method of Lines to solve the temperature field.Because this is the first to introduce parameters element of the Finite Element Method of Lines into analysis of the temperature field, so it is adopted a straight linear edge eparameterslements for solving temperature field.Through theoretical analysis, programming corresponding program of parameters element of the Finite Element Method of Lines,examples prove parameters element of the Finite Element Method of Lines not only can be used to solve the temperature field, but also has high accuracy.when solving the temperature field with parameters element of the Finite Element Method of Lines, elements-discreting and mapping of parameters element of the Finite Element Method of Lines were studied.it discretes the whole temperature field into irregular geometrical parameters elements by elements-discreting.The irregular geometrical parameters elements transfer into regular geometrical element under local coordinate system and at the same time it is established contacts between the global coordinates and local coordinates.In order to form a whole program of Finite Element Method of Lines for solving temperature field, it takes the program of parameters element of Finite Element Method of Lines to solve the temperature field into the original TFEMOL program.In the analysis of the temperature field, it can select different element according to different circumstances of the problem.