Bending, torsion and asymptotic analysis of the cantilever bar

The paper estimates deformation of elastic, statically determinate cantilever truss of the large internal volume which is subjected to bending and torsional loads for an arbitrary number of structure zones. The volume is increased by replacing flat sides of the truss with raised ones. Forces in the bars are determined analytically by cutting nodes of the truss. We derive simple analytical expressions for deflection, which allows selecting the optimal size and asymptotically compare the design flexibility to the known systems. It is shown that the flexibility of the proposed design is comparable with the known systems. Graphs, showing the dependence of the deflection on the size and the number of zones, reveal extremes, which enables optimizing the geometry of the truss. We have derived the accurate formulas for optimal parameters of the truss deflection. The induction method, supported by Maple mathematics software, is used.