Optimal Simple Structures with Bending and Membrane Stresses

Author: Giraudbit, Jean-Noël

Year: 1972

Degree: Engineer's thesis

Advisor: Babcock, Charles D.

Committee Member: Unknown, Unknown

Option: Aeronautics

DOI: 10.7907/29PJ-3X76

Abstract

Structural optimization of elastic solid structures with membrane and bending stresses is studied. A necessary and sufficient optimality condition for maximum stiffness is derived using an energy formulation (minimum potential energy). In the case of pure membrane or pure bending stress states, maximum stiffness and maximum strength are governed by the same optimality condition (uniform strength design). For mixed stress states (membrane and bending), this result is not true, and a general method of approach to find a necessary condition for maximum strength is developed by means of the calculus of variation. Two particular statically indeterminate problems with one design variable to be optimized (clamped-clamped beam, clamped-clamped arch) are treated by this method, and, in both examples, maximum. strength is achieved by a uniform strength design.

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