Optimization of plane frames by modification of fully stressed design method
Alsalloum, Yousef A.
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Permalink
https://hdl.handle.net/2142/23745
Description
Title
Optimization of plane frames by modification of fully stressed design method
Author(s)
Alsalloum, Yousef A.
Issue Date
1989
Department of Study
Engineering, General
Engineering, Civil
Discipline
Engineering, General
Engineering, Civil
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Engineering, General
Engineering, Civil
Language
eng
Abstract
In statically indeterminate frame structures, the load carried by each member is not only a function of the applied load, but in general a highly non-linear function of the relative cross-sectional properties of the members. Since the feasible region is non-convex, it is possible to have more than one local minimum each corresponding to a load-carrying mode. Each local minimum represents the optimal design for a particular mode of behavior of the structure which is a design with an efficient distribution of the material in the structure. The local minimum that represents an optimal design for a particular mode of behavior in a structure can be fully-stressed or non-fully-stressed, indicating that the design does not have to be fully-stressed to be optimal. However, the fully-stressed design method converges to the optimal design for a particular mode of behavior only when it is fully-stressed.
An algorithm based on both fully-stressed design and the Kuhn-Tucker conditions for optimality can be used to reach both fully-stressed and non-fully-stressed local minima. To obtain the non-fully-stressed local minimum, each design determined by the fully-stressed design method is forced to move to the boundary surface and then the Kuhn-Tucker conditions for optimality are employed to push the new design toward the local minimum under investigation in the design space. The fully-stressed design method is also used to identify the permanently active constraints as well as to improve the design. This algorithm and the identification of the active constraints with the help of the fully-stressed design method form a general approach to optimize stress limited frames. Several numerical examples are presented in details.
The algorithm is then extended to include displacement constraints in the formulation besides the stress constraints. A new approach called the displacement elimination approach is developed to optimize these problems. The simple fully-stressed design method also plays a major role in this approach.
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