OPTIMAL-DESIGN OF ELASTIC BEAMS FOR MOVING LOADS

The problem of minimizing the volume (weight) of an elastic beam subjected to a compliance constraint is the subject of this paper. Specifically, the necessary conditions for the minimum volume are established for the case of beams, consisting of longitudinal segments of different constant cross-sectional areas, subjected to moving loads. Two examples are considered, one for a moving concentrated load and the second for a distributed load. The results are the load location, the segment lengths and areas, and therefore the volume of the beam. For the case of the concentrated load, additional results are considered if the segment lengths are predetermined. That is, the load location and segment areas are established. The results are presented for beam cross sections that are sandwich type with different sheet thickness, solid cross sections of different widths and different depths.