## 2 Test-Case Description
### Numerical Simulation  
The finite element model of the CFRP bicycle frame was built from a 3D scan measured with a Creaform 3D scanner with an accuracy of less than 0.1 mm using the structured light principle. The resulting.stl was cleaned and used to build a 2D structured mesh of CQUAD elements within the Siemens Simcenter 11 software (Siemens PLM, Plano, Texas, US), and an overall element size of 5 mm was used. The tubes were formed by an extruded 3D mesh from the 2D mesh basis. A representation of the 2D mesh is shown in Figure 3. The laminated properties of the bicycle frame were approximated using a five-layered laminate consisting of material properties shown in Table 1:  
* a thin uniform layer of paint 0.11 mm thick;
* a CFRP layer 25% of the overall thickness with a global fiber orientation of 0\({}^{\circ}\);
* a CFRP layer 25% of the overall thickness with a global fiber orientation of 90\({}^{\circ}\);
* a CFRP layer 25% of the overall thickness with a global fiber orientation of 0\({}^{\circ}\).  
Figure 3: Overview of the 2D mesh of the bicycle frame.  
A symmetric quasi-isotropic laminate was represented as the stacking recipient. The precise stacking and layer properties are unknown, so it was assumed that the represented stacking was sufficiently accurate as an input for the material parameter optimization process, where the global thermal diffusivity properties in the thermal case and the mode shapes in the structural case are updated based on reference measurements. A detailed picture of the 3D mesh with the different layers is shown in Figure 4. The mesh consisted of 28,623 elements with a structured material orientation according to the laminate properties. The metal inserts were neglected, as they were not positioned in the vicinity of the evaluated measurement areas.  
In contrast to the mesh generation, numerical analysis was performed using Comsol Multiphysics 5.0 to facilitate interaction with the optimization routine using Matlab.  
The excitation source was modeled as a combination of two point sources. This excitation source results in a non-homogeneous spatial distributed heat excitation. The thermal time constant results in, aside from a spatial non-homogeneity, a different distribution related to the type and history of the heat source, which needed to be considered in the numerical model. The used flash excitation units are visualized in Figure 5. It can be clearly seen that the excited radiation is delayed from the initiated trigger signal due to the thermal inertia. To correlate the numerical model accurately with the experimental data, this thermal inertia will be considered as a correction (weighting) of the input signal with the thermal response.  
\begin{table}
\begin{tabular}{c c c} \hline \hline  & **Value** & **Units** \\ \hline Young’s modulus E1 & 65 & GPa \\ Young’s modulus E2, E3 & 14.9 & GPa \\ Poisson’s ratio NU12, NU23 & 0.058 & \\ Poisson’s ratio NU13 & 0.024 & \\ Shear modulus G12, G13 & 3.5 & MPa \\ Shear modulus G23 & 1.4 & MPa \\ Mass density & 1570 & Kg/m\({}^{3}\) \\ Thermal conductivity & 60 & (W/m\(\cdot\)K) \\ Thermal conductivity & 4.2 & (W/m\(\cdot\)K) \\ Specific heat capacity & 1000 & (J/(Kg\(\cdot\)K)) \\ Coefficient of convection & 10 & W/(m\({}^{2}\cdot\)K) \\ Emissivity & 0.85 & \\ \hline \hline \end{tabular}
\end{table}
Table 1: Material properties used within the numerical model.  
Figure 4: Close-up of the 3D mesh with the different plies schematically represented by different colors.