Comparable figures in mechanics - transferring model experiments for mechanical problems with linear elastic material behaviour and static loads to real components on the example of supporting structures from the field of motorsports

The development of new products is based mostly on simulations and expensive experiments. However, there are several methods to reduce experimental costs such as the utilization of the Reynolds number, a so-called comparable figure in fluid mechanics, which helps to draw conclusions about the real components from experiments with smaller components. In general, comparable figures are mainly used in the construction of ships and airplanes to get further information during the concept development stage. Solutions from construction engineering are available, as well. Nevertheless, there are currently no comparable figures available for the structural development in automotive design. Comparable figures for engineering mechanics could be used for the development of supporting structures (e.g., roll cages in motorsports, motorbike frames, etc.). The homologation of roll cages in the field of motorsports is based on quasi-static tests. This research provides comparable figures for structural mechanic problems with supporting structures based on beams (e.g., tubes). For a linear elastic material behavior, it is possible to build comparable figures for complex load cases on straight beams. There are comparable figures derived in this research for forces and moments, stress and strain, as well as for the deflection under the consideration of quasi static tests with linear elastic material behavior. For simple transient load cases (tension and bending loads) it is also shown that the comparison for each time step is possible. The laboratory experiments are based on 3D-printed plastic parts (ABS+). The difference in the internal structure of the different scaled parts is investigated, as well as an error propagation, showing a comparison of the parts. For the natural frequencies, it is also possible to build a comparable figure. These figures are based on a free vibrating beam. Unlike with static loads, small material imperfections have no significant influence on the experimental results. Therefore, the research shows the possibility of using comparable figures for structural mechanic problems of supporting structures with a constant cross-sectional area. In order to include a material influence into the comparable figure, there are approaches derived using the internal energy of a supporting structure. Further research is required to develop complete comparable figures, based on an approach using total energies.