Local radial basis function collocation method for solving thermo-mechanics of hot shape rolling of steel

Abstract

The aim of this paper is to demonstrate the suitability of the novel Local Radial Basis Function Collocation Method (LRBFCM) [1] in a coupled thermo-mechanical problem of hot shape rolling of steel. The physical concept of such a large deformation problem is based on a two dimensional traveling slice model [2], which assumes deformation and heat flow only in the perpendicular direction to rolling. The solid mechanics is, respectively, based on the steady Navier’s equation and the thermal field on the transient heat conduction equation. The displacement and traction boundary conditions are assumed in the mechanical model and Dirichlet and Neumann boundary conditions in the thermal model, both specific for hot shape rolling. The solution procedure is based on local collocation on a five noded influence domain with multiquadrics radial basis functions, augmented with the first order polynomials. The steel used in the calculations is assumed to have an ideal plastic behavior which obeys von Misses flow rule, defined by effective stress   ( , ,T) in terms of effective strain  , effective strain rate  and temperature T . The LRBFCM results of hot shape rolling of steel for a continuous 5 stand rolling mill in Štore Steel company are presented for the case of rolling of a rectangular billet with initial dimension 80 x 95 mm to a circular bar with diameter of 60 mm. The advantage of the meshless method is in accuracy and straightforward node generation, that does not require any polygonisation. The paper presents one of the increasingly emerging examples of the use of the LRBFCM in industrial applications.