Non-linear transient heat transfer analysis based on Lanczos co-ordinates using pseudo-force method

Abstract

This paper describes a reduced finite element formulation for mildly non-linear transient heat transfer analysis problems based on the Lanczos algorithm. In the proposed reduced formulation, all material non-linearities of irradiation boundary elements are included using the pseudo-force method. Numerical time integration of the reduced formulation is conducted by the Galerkin method. The results of numerical examples demonstrate the applicability and the accuracy of the proposed method for transient heat transfer analysis when restricted to mildly non-linear situations. In particular, the example of a bridge under environmental thermal condition shows that the proposed method is about 20 times faster, without loss of solution stability and accuracy, than a direct integration method for the unreduced formulation. Copyright © 1999 John Wiley & Sons, Ltd.