Absolute Minimum Weight Structures by Dynamic Programming

The structures considered herein are assumed to subject to fixed loads and design based on flexure. Furthermore, it is assumed that the cross-sectional area is proportional to the absolute value of the bending moment. The purpose of this note is to apply a sequential decision technique to minimize the area under the moment diagram directly and thereby considerably simplify the identification of the absolute minimum weight structure. The determination of the absolute minimum weight structure becomes an unconstrained minimization problem, and thus represents an entirely different approach from those that consider the kinematic or static criteria in a direct manner. Numerical solutions to a computationally difficult problem of the calculus of variations can be obtained by applying sequential decision theory. The selection of indeterminate forces as the state variables is an efficient means for describing the structural system. More general applications in absolute minimum weight design, including span length as a variable, can be formulated as dynamic programs.