## 2 The Most Used Dimensional Methods
As the authors will illustrate in the following Sections, the _MDA_ represents a simple, unitary, and particularly accessible methodology, with the following main advantages:* the involved specialist, instead of being a thorough connoisseur in the phenomenon as well as in higher mathematics, only has to identify the set of the involved variables, together with their dimensions, which have (or can present) a certain extent influence on the analyzed phenomena;
* it has a unitary, simple, and user-friendly protocol, which assures at once to automatically eliminate all insignificant/irrelevant variables;
* in all cases, _MDA_ assures obtaining the complete set of the \(\pi_{j},\ j=1\ldots n\) dimensionless variables, as well as the complete _ML_; this is practically impossible using the aforementioned methods, excepting some particular cases;
* this _ML_ is very flexible, suitable for several particular cases, corresponding to simplified approaches of the phenomena;
* by a priori setting of the directly related variables to the conceived experimental investigations on model, hereafter named _independent variables_, _MDA_ assures additional flexibility, which represents a significant advantage, non-existent in all the methods mentioned above; their a priori choice is possible both for the prototype and model;
* this set (of the independent variables) assures defining the most suitable model, which will offer for the involved model the most simple, lower-cost testing conditions, safety, as well as repeatable experimental investigations;
* the rest of the variables, hereafter named _dependent variables_, can be chosen priori only for the prototype; their magnitudes for the model are strictly obtained by applying a given (suitable) element of the _ML_;
* among the dependent variables there are also a small number of prototype variables, whose magnitude cannot be obtained more easily (with low cost or accessible experimental measurements) and whose determination is actually the purpose of this dimensional analysis; thus, these aforementioned prototype's variables are obtained by applying the _ML_;
* furthermore, _MDA_ removes the restriction of the geometric similarity of the model with the prototype, e.g., the shape of the cross-sections can be different at the model from the prototype; in this case, instead of choosing the cross-sectional dimensions as independent variables, one will substitute them by the \(I_{z}\) second order moment of inertia of the cross-section;
* if the material is considered as an independent variable, chosen by means of \(E\) Young modules, then one can accept different materials for the model, relative to the prototype;
* in the case of choosing the \(E\cdot I_{z}\) flexural stiffness (rigidity) instead of the cross-sectional dimensions, than neither the shape of the cross-section, nor the type of material must be identical in the prototype and model; the single condition remaining is that their \(S_{E\cdot I_{z}}\) scale factor must remain the same (to be constant), where this scale factor is defined as the ratio of the \(E\cdot I_{z}\) flexural stiffnesses, that is, \(S_{E\cdot I_{z}}=\frac{E_{2}\cdot I_{z,2}}{E_{1}\cdot I_{z,1}}\), with the aforementioned indexing (2 for model, and 1 for prototype). Of course, this evaluation can be continued, but only these aforementioned facilities underline the suitability of _MDA_ in _AM_ process optimization. In addition, readers can obtain additional information in applying the _MDA_ facilities in different engineering applications from [94; 95; 120; 121; 122]. In Section 3, the authors offer an overview on the dimensional methods' involvement in different aspects of Additive Manufacturing.