Reduction methods for nonlinear steady-state thermal analysis

A hybrid reduction algorithm for the FEM analysis of nonlinear steady-state temperature distributions in structures and solids is developed and applied. The number of degrees of freedom of the initial FEM discretization is reduced by expressing the unknown-nodal-temperature vector as a linear combination of global-temperature modes (perturbation-technique path-derivative basis vectors) whose amplitudes are calculated by a Bubnov-Galerkin procedure. The technique is applied to 2D steady conduction in a square plate and in a cylinder with an eccentric hole; to 1D steady conduction, convection, and radiation in a fin; and to steady conduction and radiation in a Space Shuttle orbiter-wing segment. The results of single-parameter and multiparameter analyses are presented graphically, demonstrating the accuracy and efficiency of the method.