Two-dimensional transient FEM （finite element model） for heat transfer and elastic-plastic stress of liquid steel solidification in continuous casting round mould was established based on the ANSYS software

in which from the essential phenomena in the mould

a gas gap-dependent heat transfer condition were introduced to modify the heat flux function

and the variation of material thermal properties

mechanical properties as well as yield function with temperature were considered. Based on secondary development for the model

using multi-field indirect coupled method

the solidification shrinkage process of four kinds of round steel billets were simulated. The results reveal that solidifications shrinkage is closely related to steel types

carbon content and drawing velocity. Mould taper exhibits continuous parabolic curves along the height of the mould. At the outlet of mould

the solidification shrinkage rates of four round billets make 2.2 mm

3.41mm

3.79 mm and 4.30 mm

respectively. Based on the solidification shrinkage curves of round billets and basic principle of mould design

the universal parabolic taper for round mould is completed.