Designing branching or shaped composite elements by analogy with the structure of treetops

Abstract

The analogy of the bending flexibility of shaped beams of the constarea class (with a constant area of the cross section) and branching composite structures that resemble a treetop with a constant sum of the areas of sections of the branches (Leonardo’s rule) has been studied. Ideally, profiling or branching provide threefold growth in flexibility while retaining strength, i.e., a threefold increase in the accumulated elastic energy for the fixed load and mass of the elastic element. It has been shown that the use of the fiberglass in these elastic elements enables one to reduce their mass by approximately 20 times compared to the steel analog. The limitation of the possibility of use of the linearized bend equation for the shaped beams has been specified. The efficient use of branching composite elastic elements is possible in space-based structures due to their light specific weight and extremely low energy consumption when producing parts from polymer composites, which allows them to be produced directly in orbit.