| The requirements for minimum-weight structures were developed by A. G. M. Michell whose work was extended from Maxwell's Theorem. The similarity of structure problems and metal deformation problems allows the solution of Michell layouts by using slip-line field theory. Matrix operator methods were applied to determine shapes of tension and compression members for a variety of minimum-weight structures. Application examples are given, including torsion wheels, basic cantilevers, extended cantilevers and simply-supported beams.; Numerical procedures were established to find structure layouts by using MatLab as the programming language with the use of matrix operators. The analysis for a framework as a truss was used to determine internal forces for the structure members. In order to obtain uniform stress and strain distributions required by Michell's theorem, the thickness dimensions were computed in proportion to the forces they carry. Solid models were then created in CAD software and imported into a rapid manufacturing machine to make prototypes for visualization and testing purposes.; In general, a basic cantilever is defined by its depth, length and width. An optimization technique is therefore applied to define design variables from the engineering information to minimize errors of desired and generated geometries.; A simply-supported symmetrical beam with a constant height was loaded in compression in the testing machine. An I-beam, occupying the same volume, having the same space and made from the same material, was also subjected to the same loads.{09}The results show that the deflections of the Michell beam are close to the theoretical predictions and the Michell beam is substantially stronger than the I-beam. |
