Structural Optimization by Inscribed Hyperspheres

by Roman Baldur, Res. Prof.; Div. of Applied Mechanics, Ecole Polytechnique, Montreal, Quebec, Canada,

Serial Information: Journal of the Engineering Mechanics Division, 1972, Vol. 98, Issue 3, Pg. 503-518

Document Type: Journal Paper


A procedure is suggested for optimization of a function by an iterative process which converges through a series of intermediate solutions tending to be as far removed as possible from the constraint boundaries. Each iteration is based on a linearization of the objective function and the constraint equations. This leads to the solution for the freest point defined as the center of the largest hypersphere which can be inscribed inside the feasible region. The calculation technique is based on well known linear programming methods. Several illustrative examples are given and a geometric interpretation of the procedure is included. This method is particularly advantageous where a mixture of mathematical and intuitive steps must be applied.

Subject Headings: Linear functions | Domain boundary | High-rise buildings | Computer programming | Geometrics | Mixtures | Optimization models

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