Harmonic Shape and Optimum Design

by Rowland Richards, Jr., (M.ASCE), Prof.; State Univ. of New York, Buffalo, N.Y.,
Gordon S. Bjorkman, Jr., (A.M.ASCE), Struct. Engr.; United Engr. and Constructors, Inc., Philadelphia, Pa.,

Serial Information: Journal of the Engineering Mechanics Division, 1980, Vol. 106, Issue 6, Pg. 1125-1134

Document Type: Journal Paper


The harmonic condition and strategy for the inverse design problem in elasticity is examined. The analogy to membrane shapes and free-surface potential flow problems due to the irrotational character of the perturbations introduced by harmonic shapes is highlighted. Basic equations for the interior problem for holes and inclusions are derived using the complex variable formulation. They are than applied to determine the harmonic shape for a rigid inclusion in a biaxial field which is shown to be optimum giving the minimum possible stress concentration.

Subject Headings: Plastic design | Elastic analysis | Membranes | Free surfaces | Potential flow | Biaxial strength

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