On minimum weight design of statically loaded continuous beams with deflection constraints

TLDR: In this article, the authors considered the optimum design of elastic continuous beams of solid crosssection, subjected to static loading, and the deflection at a given point along the beam, is specified.

Abstract: The paper is concerned with optimum design of elastic continuous beams of solid crosssection, subjected to static loading. The deflection at a given point, along the beam, is specified. Assuming a rectangular cross-section and taking the thickness as the design variable, the thickness variation is sought as to make the weight of the beam a minimum. In the formulation, an energy concept is used. A numerical example is given for illustration.