Application of the fully automatic 3D hp adaptive code to orthotropic heat transfer in structurally graded material properties

The prime objective of the paper is the application of the fully automatic hp adaptive Finite Element Method (FEM) code to solve heat transfer problems over the domain with various materials. Large changes in material data generate singularities: non-continuities or large gradients of the solution to the heat equation. To minimize the error of FEM solution the mesh should be refined close to the singularities by sub-dividing elements and increasing the polynomial order of approximation. It is very difficult to design an optimal hp mesh by hand. This paper presents a typical application of the fully automatic 3D hp adaptive FE code to the problem of modelling of the resistance heating of an Al–Si billet in a steel die for thixoforming process. The code automatically produces an FE mesh with minimal number of degrees of freedom, resolving all singularities within a prescribed error tolerance.