A LEAST SQUARES METHOD FOR CONSTRAINED MINIMIZATION WITH APPLICATION IN STRUCTURAL DESIGN
Abstract
A technique for constrained parameter optimization is presented and applied to some test problems. The procedure employs an exterior penalty function to transform the constrained objective function into an unconstrained index of performance which is minimized by Gauss' method. Gauss' method recasts the minimization problem to one of solving simultaneous linear equations with the variation of the parameters as the unknowns. For the special case of a quadratic objective function and linear constraints, the penalized critical value is obtained in one step. The restriction that the objective function be of least squares form results from using Gauss' method. The restriction on each constraint is that first derivatives with respect to all parameters be obtainable. A modified version of the technique is applied to the minimum-mass design of truss type structures. The modifies technique is first applied to several standard problems demonstrating its relative efficiency and accuracy. Next, the standard problems are altered to introduce local buckling constraints and new designs are obtained. It is shown these designs also satisfy global stability. Finally, to demonstrate the methods capabilities, static thermal loads are introduced and an equality constraint is imposed on the fundamental natural frequency of each structure. The natural frequency analysis uses a four degree of freedom element.
Degree
Ph.D.
Subject Area
Aerospace materials
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