Date of Award

Summer 1995

Document Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical & Aerospace Engineering


Engineering Mechanics

Committee Director

Gene Hou

Committee Member

Charles Camarda

Committee Member

Chuh Mei

Committee Member

Duc Nguyen


The force-derivative method (FDM) represents a series of higher-order modal methods which offer an increasingly improved approximation of the higher modes neglected in the basic mode-displacement method (MDM). The FDM includes additional terms which involve the forcing function and derivatives of the forcing function with respect to time. The mode-acceleration method (MAM), extensively used in structural analysis, is a first-order form of the FDM which includes only one correction term that depends on the forcing function itself. The success of the FDM in many structural dynamic applications has prompted its application for solving transient thermal problems. The superior convergence of the FDM for a one-dimensional linear transient thermal problem has been demonstrated in the past. The primary focus of this study is therefore on the application of the FDM as a reduction technique for solving nonlinear transient thermal problems. A new finite element algorithm, which incorporates the modal methods and a fixed-point iteration scheme, has been developed and implemented in the COmputational MEchanical Testbed (COMET). The role played by the correction terms of the higher-order methods in improving the convergence of the modal methods (in terms of the number of modes required) and the parameters that influence them are identified. Finally, results of a two-dimensional model of the lower surface of the Shuttle wing segment with complex heating profiles are presented which demonstrate the applicability and the effectiveness of the FDM for solving nonlinear transient thermal problems.