Reduction methods for nonlinear steady-state thermal analysis

Hybrid analysis techniques and a problem adaptive computational algorithm are presented for predicting the nonlinear steady state temperature distribution in structures and solids. In the proposed techniques, the structure is discretized by using the finite element method. The vector of nodal temperatures is then expressed as a linear combination of a small number of global temperature modes (or basis vectors), and the Bubnov Galerkin technique is used to compute the amplitudes of the global modes. The global temperature modes (or basis vectors) are chosen to include the various order derivatives of the nodal temperature vector with respect to preselected path parameter(s). The potential of the proposed reduction methods for solution of large scale, nonlinear thermal problems is discussed and the effectiveness of the methods is demonstrated by means of numerical examples, including steady state conduction, convection, and radiation modes of heat transfer.