Structural Optimization Using Geometric Programming and the Integrated Formulation
Burns, Scott Allen
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https://hdl.handle.net/2142/69943
Description
Title
Structural Optimization Using Geometric Programming and the Integrated Formulation
Author(s)
Burns, Scott Allen
Issue Date
1985
Department of Study
Civil Engineering
Discipline
Civil Engineering
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, Civil
Abstract
The possibility of solving the "integrated" formulation of structural optimization is investigated. Structural behavior relationships, equilibrium and compatibility, are treated as explicit equality constraints and the problem solved as a large scale nonlinear mathematical programming problem. In contrast to current methods of optimization where analysis and design are separated into two distinct phases, the integrated approach does not distinguish between the two activities. Because of the large size of the resulting problem, solution by the currently available nonlinear mathematical programming methods is impractical. An extension of the Generalized Geometric Programming method is developed that handles nonlinear equality constraints efficiently. It is shown that the method is similar to the Newton-Raphson method and is carried out simultaneously with the cutting plane process of Generalized Geometric Programming. The efficiency of the resulting method stems from its use of linear programming, for which increasingly efficient methods of solution are constantly being developed. The method does not, however, suffer from the usual problems encountered with a simple linearization of a nonlinear problem, i.e., nonconvergence due to nonconvexity. The method presented here first isolates a convex subset of the possibly nonconvexfeasible region. The Generalized Geometric Programming method generates a series of such convex regions that converge to a solution of the overall problem.
The method is applied to two classes of structures, framed and continuum structures. A three story, two bay frame and several variable depth beams are presented as examples of the method.
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