A Steady-State Thermomechanical Solution of Continuously Quenched Axisymmetric Bodies

Abstract

A finite element methodology to solve steady-state thermochemical problems is presented in this paper, where axisymmetric geometry is considered, and small strain and small rotation are assumed for the mechanical problem. Both thermal and mechanical problems are formulated in the Eulerian frame with the finite element method. The heat transfer problem is solved with the Petrov-Galerkin method due to the convection-diffusion nature of the governing equation, and the virtual work principle is applied to the equation of motion to obtain the finite element formulation. To determine the inelastic deformation, an additional system of equations is formed by applying the Petrov-Galerkin method to the material derivatives of the inelastic strain rates. Studies in this paper focus on continuous axisymmetric problems with quenching examples. Generally, the computational time with the steady-state (Eulerian) method presented in this paper is significantly less than that with transient (Lagrangian) approaches.