Designing light-weight structures consisting of multiple elements loaded in bending

The aggregation method for designing light-weight structures consists of consolidating multiple loaded elements into fewer elements with larger cross-sections under the same total load. This approach is very effective for beams with arbitrary cross-sectional shapes and leads to a significant reduction in the material required to support a given total load. For instance, in a five-to-one aggregation, the material usage is reduced by a factor of 1.71. The theoretical foundations of the method of aggregation have been rigorously developed and proven, specifically for structures composed of beams with arbitrary cross sections. Additionally, finite element simulations and experimental testing on statically indeterminate structures validated the method and confirmed its effectiveness. These investigations demonstrated that aggregating loaded elements substantially increases load-bearing capacity while reducing material consumption. It has also been established that segmenting multiple loaded beams into a larger number of beams, under the same total load, increases the total elastic strain energy of the structure. This result holds true for arbitrary cross-sectional shapes. Finally, an interpolation method has been proposed for reducing the total volume of material at a specified maximum von-Mises stress and maximum deflection.