Adaptive Optimal Shapes of Beam and Arch Structures by the Growing Reforming Procedure

Abstract

A Growing-Reforming Procedure has been proposed in the previous paper. First, in this paper, some applications of the Growing-Reforming Procedure to beam structures are shown. The shapes with uniform strength are obtained by this procedure. Some applications are shown for (1) a cantilever beam loaded uniformly along the span, (2) a fixed-end beam loaded at the center, (3) a fixed-end beam loaded uniformly, (4) a spatially restricted beam with the same conditions as (3), (5) a fixed-end beam with an extended evaluation of shearing stress. Next, a modified method of forming arch structures is presented. This modified method is applied to some typical problems. Comaprison of beam structures with arch structures is made. The features of the obtained shapes are discussed.