On the value of Guyan Reduction in dynamic thermal problems

Abstract

In one dimension, the Guyan Reduction of a linear finite element approximation is shown to be equivalent to the use of a cruder linear finite element approximation in dynamic thermal problems. The method of proof for one dimension does not carry over to higher dimensions. In lieu of this, a transient two dimensional problem with realistically chosen physical constants is numerically analyzed for three different boundary conditions. The bilinear finite element approximations for each boundary condition case are computed for a given uniform mesh, as well as the corresponding approximations for a naturally chosen cruder mesh. Also, the approximations acquired by the Guyan Reduction of the initial mesh to the cruder mesh are computed. For each boundary condition case, the cruder finite element approximation was much closer to the original approximation than was the Guyan reduction. In addition, a wide variety of other Guyan Reduction approximations were computed and only one had answers as good as the cruder finite element approximation.