International Journal of Physical Sciences Vol. 2 (1), pp. 018-032, January 2007          
ISSN 1992-1950 © 2007 Academic Journals

Full Length Research Paper

Precision of sensitivity in the design optimization of indeterminate structures

Surya N. Patnaik^1*, Shantaram S. Pai² and Dale A. Hopkins²

¹Ohio Aerospace Institute, Brook Park, OH 44142, U.S.A.

²National Aeronautics and Space Administration, Glenn Research Center, Cleveland, OH 44135, U.S.A.

*Corresponding author. E-mail: surya.n.patnaik@nasa.gov. 

Accepted 19 January, 2007

Design sensitivity is central to most optimization methods. The analytical sensitivity expression for an indeterminate structural design optimization problem can be factored into a simple determinate term and a complicated indeterminate component. Sensitivity can be approximated by retaining only the determinate term and setting the indeterminate factor to zero. The optimum solution is reached with the approximate sensitivity. The central processing unit (CPU) time to solution is substantially reduced. The benefit that accrues from using the approximate sensitivity is quantified by solving a set of problems in a controlled environment. Each problem is solved twice: first using the closed-form sensitivity expression, then using the approximation. The problem solutions use the CometBoards testbed as the optimization tool with the integrated force method as the analyzer. The modification that may be required, to use the stiffness method as the analysis tool in optimization, is discussed. The design optimization problem of an indeterminate structure contains many dependent constraints because of the implicit relationship between stresses, as well as the relationship between the stresses and displacements. The design optimization process can become problematic because the implicit relationship reduces the rank of the sensitivity matrix. The proposed approximation restores the full rank and enhances the robustness of the design optimization method.

Key words: Approximate sensitivity, design, optimization, singularity, implicit relationship, indeterminate structure.