Two quasi-optimal solutions for uniform load between two supports

Abstract

Two frameworks for the title problem are presented, for the half and full plane cases respectively, with semi-analytical layouts. It is shown that both are among the best layouts obtained by several methods, including Simulated Annealing (SA) search and Linear Programming (LP). Respectively, the heights are found to be 0.442 and 0.633 times the span L. The required volume of material is given by V = kwL2/f where w is the load intensity and f the allowable stress, being k respectively equal to 0.985 and 0.758. The corresponding results for the layouts on the basis of the one presented by W. Hemp in 1974 are 0.338L, 0.676L, 1.158wL2/f, and 0.788wL2/f. None of these frameworks meets the conditions of Michell theorem, hence there is not sound proof that they are absolute optima. The meaning of this fact is discussed and two future lines of research are proposed.