## 1 Modern Dimensional Analysis Model Laws Used to Model Additive Manufacturing Processes  
**[PERSON] 1, [PERSON] 1,*\({}^{\copyright}\), [PERSON] 1\({}^{\copyright}\), [PERSON] 1,2,*\({}^{\copyright}\), [PERSON] 1, [PERSON] 1 and [PERSON] 1**  
1 Department of Mechanical Engineering, Transylvania University of Brasov, B-dul Eroilor 29, 500036 Brasov, Romania; [EMAIL_ADDRESS] (Z.A.); [EMAIL_ADDRESS] (M.-L.S.); [EMAIL_ADDRESS] (B.-P.G.); [EMAIL_ADDRESS] (S.R.-L.); [EMAIL_ADDRESS] (G.F.)
2 Technical Sciences Academy of Romania, B-dul Dacia 26, 030167 Bucharest, Romania
* Correspondence: [EMAIL_ADDRESS] (I.S.); [EMAIL_ADDRESS] (S.V.)  
**Featured Application: Additive Manufacturing (_AM_) represents new and very promising manufacturing processes. The results can be applied immediately in the manufacturing industry in order to obtain significant decreases of the costs in some specific domains.**  
**Abstract:** By means of its facilities, \(AM\) brings several advantages in comparison with the classical manufacturing technologies. Nowadays, there are a huge number of unexplored directions, which assure \(AM\) will become a very powerful manufacturing process in the next period, with an undoubted low cost and reduced material consumption, as well as optimal stiffness and competitiveness technology. Between the unexplored (or less-explored) directions, one has to mention the dimensional methods' involvement in gaining an optimal, highly competitive final product. This means that instead of the real structural element, named the prototype, the engineers will perform high-accuracy tests on the attached reduced-scale models, whose experimental results are extended to the prototype by means of the deduced model law (_ML_). The authors, based on their previous theoretical research as well as experimental investigations, offer a new approach, which is less implemented in \(AM\) technologies. Based on the obtained results, these dimensional methods are very promising, especially the last one, the so-called Modern Dimensional Analysis (_MDA_), conceived by [PERSON] and described in the following paper. Starting with the nowadays-applied dimensional methods' critical analysis, the authors will present evidence for the advantages of \(MDA\), especially on the polymer-based \(AM\) technology. They will prove that \(MDA\) represents a very promising, as well as easy approach, which through its implementation can offer a higher competitiveness for \(AM\) technologies. As an illustration of the advantages of \(MDA\), the authors conceived several \(MDA\) approaches for a given structural element's case (a cantilever beam, with an internal-ribbed structure loaded at its free end by means of a vertical concentrated load), which, through their high accuracy in experimental-validated \(ML\)s, offer very good accuracy in model-prototype correlation. The deviations between the effective measured values of the displacements on the prototypes and those predicted, based on the values of the measurements on the models assigned to the prototypes by the validated MLs, were 1.06, 1.60, and 2.35%, respectively. In the authors' opinion, \(MDA\) can represent a starting point for conceiving a highly competitive product with an optimal filling, as well as the deposition of layers using \(AM\) technologies. Based on the authors' best knowledge, up to this moment, it seems that this engineering area does not fully apply the advantages of \(MDA\), only in few limited cases, analyzed in the following.**  
**Keywords:** additive manufacturing; dimensional analysis; geometric analogy; theory of similarity; structural optimization