# Methodology for the Concept Design of Locally Reinforced Composites
## 2 Approach and Models
### Economic Model  
The presented economic model aims for the cost estimation of composite structures in an early phase of the product development process. Within this economic model, only the manufacturing steps of cutting and stacking are considered, and subsequent steps such as preforming are not considered, since only plane and rectangular structures, as introduced in Section 2.1, are assessed within this paper. Subsequently, the cost model can be replaced by company-specific cost models. Available models from the state of the art are not applicable for TT, since they do not consider the split between base-laminate and reinforcements. Hence, a simplified approach for the estimation of TT costs is introduced. To unravel the economic influences of the previously introduced mechanical model, the same patch laying manufacturing method is considered, to ensure the comparability of the results. This model focuses only on the manufacturing of the fabric semi-finished product, including material costs, waste costs, cutting costs, and stacking costs (see Equation (1)).  
\[\mathrm{C_{total}}=\sum_{n}\left(\mathrm{C_{material,n}}+\mathrm{C_{waste,n}}+ \mathrm{C_{cutting,n}}+\mathrm{C_{stacking,n}}\right) \tag{1}\]  
The subsequent manufacturing steps are assumed to be within the same cost range for each laminate concept, and therefore not given further consideration. The input parameters passed from the mechanical model are the material data and the dimensions of the reinforcements (reinforced area and number of clusters). Hence, only the relative cost-proportion between the different concepts is considered; the average costs for material, waste, cutting, and stacking are applied within the presented model. Stacking costs for a manual lay-up process can be described as labor costs, depending on the patch size. For example, smaller patches are easier to handle, but more working steps are required to cover a certain area compared to larger patches. This results in higher costs per area for small patches. By applying a best-fit curve to the empirical data collected within the research project \"Tailored Composites\", formula (2) can be deduced. Formula (2) allowscalculating the patch size depending on stacking costs. The prepositioned factor, as well as the exponent, cover a constant cost share, resulting from the empirically measured stacking times required for certain patch sizes (see Figure 6).  
\[c_{\text{stacking,i}}=37.023\cdot\text{A}_{patch,i}{}^{-0.685} \tag{2}\]  
Waste costs are composed of an average general waste percentage of 5% and the cut-off resulting from trimming the fabric multiplied by the material density and costs (Equation (3)).  
\[\text{C}_{\text{i,Waste}}{=}\text{C}_{\text{i,Material}}{\cdot}\rho_{i}{\cdot} \text{A}_{\text{i,Waste}}{\cdot}(100\%+\text{c}_{\text{i,percent\_ waste\_ general}}) \tag{3}\]  
The calculation of the waste area and hence the waste cost calculation, as presented in this paper, is applicable for any components made of a single or multiple rectangular fiber patches. However, within this approach a square-shaped demonstrator is considered (see Section 3), resulting in the trimmed waste of the inner circular cut-out and the outer cut-offs. The outer cut-offs are dependent on the fabric's fiber orientation relative to the cutting edges (c.f. Figure 7, Equation (4)). Assuming the reinforcement patches are orientated at 0\({}^{\circ}\), only the general waste ratio is considered.  
\[\text{A}_{\text{i,Waste}}=\Big{(}\text{width}_{\text{i,Phy}}{}^{2}{+}\text{ length}_{\text{i,Phy}}{}^{2}\Big{)}{\cdot}\sin{\alpha}{\cdot}\cos{\alpha} \tag{4}\]