Efficient Solution Processes for Finite Element Analysis of Transient Heat Conduction

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Abstract
Systematic procedures are presented for reducing the order of a matrix differential equation governing transient heat conduction in solids. Two principal aspects of this development are a condensation of the set of gridpoint temperature degrees of freedom using steady-state relations and the introduction of generalized (modal) temperature degrees of freedom to achieve a further reduction. These processes are illustrated in an elementary one-dimensional transient heat conduction problem.

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