Date of Award

Spring 2001

Document Type

Dissertation

Degree Name

Doctor of Philosophy in Civil Engineering - (Ph.D.)

Department

Civil and Environmental Engineering

First Advisor

William R. Spillers

Second Advisor

C.T. Thomas Hsu

Third Advisor

M. Ala Saadeghvaziri

Fourth Advisor

John R. Schuring

Fifth Advisor

John Tavantzis

Abstract

This work is driven by recent developments in mathematical programming, the state-of-the-art of structural optimization, the spectacular performance of linear programming algorithms, and computer hardware developments which imply that applications of structural optimization might be used commonly in engineering design. Currently, there are few general purpose optimization routines available to the structural engineer and much of the work has addressed specific classes of problems. Further, there is little widespread use of the available routines, partly due to the large amount of familiarity one must have with the specific details of both the problem and the optimization method. In response, it is the intention here to prototype a software system that implements a general approach for structural optimization using the latest in mathematical programming techniques.

This work develops a general system that can be used for a variety of structural optimization problems in a manner analogous to the finite element method for structural analysis. The most commonly used structural elements, truss and beam, are included as well as techniques for plate optimization. Consideration is given to the software requirements of a general purpose structural optimization system and the demands of large structural systems typically encountered in design practice.

This general approach is aimed at using classical methods taken directly from the area of mathematical programming, specifically linear programming, which has seen considerable change in the last ten years. Here, sequential linear programming (SLP) techniques are shown to handle a wide variety of structural constraints including stress constraints, displacement constraints, buckling, and frequency constraints. It is the purpose of this thesis to bring the latest developments in linear programming to the field of structural optimization in the form of a general purpose, state-of-the-art structural optimization system. The model was tested for sample structures and it was shown to effect a reduction in total structure volume of up to 80%.

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