Abstract
The problem of minimizing the volume (weight) of an elastic beam subjected to moving loads and to an imposed maximum deflection is the subject of this paper. Specifically, by means of the calculus of variations, the necessary conditions for the minimum volume are established for beams consisting of longitudinal segments of constant cross-sectional area. Two examples are considered, one for a moving concentrated load and the second for a moving distributed load. The results, at optimum, are the load location, the location of the maximum prescribed displacement, the segment lengths, and areas, and consequently the volume of the beam. For the case of the concentrated load, additional results are obtained for predetermined segment lengths. The results are presented for beam cross sections that are of the sandwich type, and for solid cross sections of different widths or depths.
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