Study of material interpolation for 3D lightweight structures

The use of computer tools has become essential in modern engineering, from the use of specific software to programming it. That is why this work seeks to provide the tools to understand the essential knowledge of programming for a modern engineer, which allows the easy correction, understanding and efficiency of the code. In addition, the thesis seeks to solve one of the heuristic problems of topology optimization. It is a research field that obtains optimal design structures in terms of volume usage. The most popular approach, the SIMP method, an auto-penalized interpolation function in a relaxed topology optimization problem, does not always propose actual solutions. For this reason, an alternative solution to the SIMP method is to be found for any case scenario. Finally, it is intended to apply these knowledge by rewriting part of the Swan code. By refactoring a previously programmed code from the subject ’aerospace structures’, called ”Codi Cante”, the sections object oriented programming, work with cloud backups, test driven development and clean code are developed. These are tools used by modern software engineers. Regarding topology optimization, an alternative method called SIMP-All is used to solve the drawbacks of the SIMP method. From the previously defined methods, knowledge is acquired to program efficiently and structurally. At this point, object oriented programming, cloud-backed work, test driven development and clean code are discussed. On the other hand, the results concerning topology optimization allow the obtaining of optimal and actual structures. Firstly, the SIMP-All method solution for three-dimensional cases is found. The solution is then shown to be part of the physical limits called ”Hashin-Shtrikman bounds” and a comprehensive solution for the SIMP-All method is proposed. These results are compared with the SIMP method in two and three dimensions. Finally, all the new knowledge is applied to rewrite part of the Swan code. In conclusion, from the refactoring of the ”Codi Cante”, sufficient tools have been developed to understand essential knowledge of programming by a modern engineer. Besides that, it has been possible to obtain a general equation for the SIMP-ALL method. Not only does the generalized equation allow to find optimal results, but the generated structures are also possible in the reality. Furthermore, the equation has been implemented in the Swan program using the new programming knowledge, thus allowing an easy correction, understanding and efficiency of the code