**Figure 1.**
Exploded view of a three-layered fibre-reinforced composite material.

**Figure 1.**
Exploded view of a three-layered fibre-reinforced composite material.

**Figure 2.**
Matrix plot of the modelling parameters and the resulting maximum deflection $({\mathrm{w}}_{\mathrm{max}})$ and fundamental frequency $({\mathrm{f}}_{1})$ (unidirectional plate, a/h = 20, all input parameters uncertain).

**Figure 2.**
Matrix plot of the modelling parameters and the resulting maximum deflection $({\mathrm{w}}_{\mathrm{max}})$ and fundamental frequency $({\mathrm{f}}_{1})$ (unidirectional plate, a/h = 20, all input parameters uncertain).

**Figure 3.**
Matrix plot of the maximum deflection $({\mathrm{w}}_{\mathrm{max}}(\mathrm{m}))$ for different sets of uncertain parameters (unidirectional plate, a/h = 20).

**Figure 3.**
Matrix plot of the maximum deflection $({\mathrm{w}}_{\mathrm{max}}(\mathrm{m}))$ for different sets of uncertain parameters (unidirectional plate, a/h = 20).

**Figure 4.**
Matrix plot of the modelling parameters and the resulting maximum deflection $({\mathrm{w}}_{\mathrm{max}})$ and fundamental frequency $({\mathrm{f}}_{1})$ (unidirectional plate, a/h = 20, all modelling parameters uncertain except the ply thickness).

**Figure 4.**
Matrix plot of the modelling parameters and the resulting maximum deflection $({\mathrm{w}}_{\mathrm{max}})$ and fundamental frequency $({\mathrm{f}}_{1})$ (unidirectional plate, a/h = 20, all modelling parameters uncertain except the ply thickness).

**Figure 5.**
Matrix plot of the stacking angles (θ_{1}–θ_{4}) and the resulting maximum deflection $({\mathrm{w}}_{\mathrm{max}})$ and fundamental frequency $({\mathrm{f}}_{1})$ for Case 1.a (a/h = 20, [0]_{4}).

**Figure 5.**
Matrix plot of the stacking angles (θ_{1}–θ_{4}) and the resulting maximum deflection $({\mathrm{w}}_{\mathrm{max}})$ and fundamental frequency $({\mathrm{f}}_{1})$ for Case 1.a (a/h = 20, [0]_{4}).

**Figure 6.**
Matrix plot of the maximum transverse displacement $({\mathrm{w}}_{\mathrm{max}})$ considering different sets of uncertain stacking angles for Case 1.a (a/h = 20, [0]_{4}).

**Figure 6.**
Matrix plot of the maximum transverse displacement $({\mathrm{w}}_{\mathrm{max}})$ considering different sets of uncertain stacking angles for Case 1.a (a/h = 20, [0]_{4}).

**Figure 7.**
Matrix plot of the maximum transverse displacement $({\mathrm{w}}_{\mathrm{max}})$ considering different sets of uncertain stacking angles for Case 2.a (a/h = 100, [0]_{4}).

**Figure 7.**
Matrix plot of the maximum transverse displacement $({\mathrm{w}}_{\mathrm{max}})$ considering different sets of uncertain stacking angles for Case 2.a (a/h = 100, [0]_{4}).

**Figure 8.**
Matrix plot of the maximum transverse displacement $({\mathrm{w}}_{\mathrm{max}})$ considering different sets of uncertain stacking angles for Case 2.b (a/h = 100, [0/90]_{S}).

**Figure 8.**
Matrix plot of the maximum transverse displacement $({\mathrm{w}}_{\mathrm{max}})$ considering different sets of uncertain stacking angles for Case 2.b (a/h = 100, [0/90]_{S}).

**Figure 9.**
Matrix plot of the maximum transverse displacement $({\mathrm{w}}_{\mathrm{max}})$ considering different sets of uncertain stacking angles for Case 1.c (a/h = 20, [0/90]_{2}).

**Figure 9.**
Matrix plot of the maximum transverse displacement $({\mathrm{w}}_{\mathrm{max}})$ considering different sets of uncertain stacking angles for Case 1.c (a/h = 20, [0/90]_{2}).

**Figure 10.**
Matrix plot of the ply thicknesses (h_{1}–h_{4}) and the resulting maximum deflection $({\mathrm{w}}_{\mathrm{max}})$ and fundamental frequency (f_{1}) for Case 3.a (a/h = 20, [0]_{4}).

**Figure 10.**
Matrix plot of the ply thicknesses (h_{1}–h_{4}) and the resulting maximum deflection $({\mathrm{w}}_{\mathrm{max}})$ and fundamental frequency (f_{1}) for Case 3.a (a/h = 20, [0]_{4}).

**Figure 11.**
Matrix plot of the maximum transverse displacement $({\mathrm{w}}_{\mathrm{max}})$ considering different sets of uncertain ply thicknesses for Case 3.c (a/h = 20, [0/90]_{2}).

**Figure 11.**
Matrix plot of the maximum transverse displacement $({\mathrm{w}}_{\mathrm{max}})$ considering different sets of uncertain ply thicknesses for Case 3.c (a/h = 20, [0/90]_{2}).

**Figure 12.**
Matrix plot of the maximum transverse displacement $({\mathrm{w}}_{\mathrm{max}})$ considering different sets of uncertain ply thicknesses for Case 4.b (a/h = 100, [0/90]_{S}).

**Figure 12.**
Matrix plot of the maximum transverse displacement $({\mathrm{w}}_{\mathrm{max}})$ considering different sets of uncertain ply thicknesses for Case 4.b (a/h = 100, [0/90]_{S}).

**Figure 13.**
Residuals of the regression model for ${\mathrm{w}}_{\mathrm{max}}$ (Equation (8)).

**Figure 13.**
Residuals of the regression model for ${\mathrm{w}}_{\mathrm{max}}$ (Equation (8)).

**Table 1.**
Carbon fibre prepreg laminate properties (IM7/8552 UD Hexcel composites).

**Table 1.**
Carbon fibre prepreg laminate properties (IM7/8552 UD Hexcel composites).

${\mathbf{E}}_{\mathbf{11}}$ (GPa) | ${\mathbf{E}}_{\mathbf{22}}\mathbf{,}{\mathbf{E}}_{\mathbf{33}}$ (GPa) | ${\mathbf{G}}_{\mathbf{12}}\mathbf{,}{\mathbf{G}}_{\mathbf{13}}$ (GPa) | ${\mathbf{G}}_{\mathbf{23}}$ (GPa) | ${\mathsf{\nu}}_{\mathbf{12}}\mathbf{,}{\mathsf{\nu}}_{\mathbf{13}}$ | ${\mathsf{\nu}}_{\mathbf{23}}$ | $\mathsf{\rho}$ (kg/m^{3}) |
---|

161 | 11.38 | 5.17 | 3.98 | 0.32 | 0.44 | 1500 |

**Table 2.**
Case studies with uncertain stacking angles $({\mathsf{\theta}}_{\mathrm{ply}})$.

**Table 2.**
Case studies with uncertain stacking angles $({\mathsf{\theta}}_{\mathrm{ply}})$.

Case | $\mathbf{a}\mathbf{/}\mathbf{h}$ | Stacking Sequence | ${\mathsf{\mu}}_{{\mathsf{\theta}}_{\mathbf{p}\mathbf{l}\mathbf{y}}}$ | ${\mathsf{\sigma}}_{{\mathsf{\theta}}_{\mathbf{p}\mathbf{l}\mathbf{y}}}$ |
---|

1.a | 20 | [0]_{4} | nominal values | 2° |

1.b | [0/90]_{s} |

1.c | [0/90]_{2} |

2.a | 100 | [0]_{4} | nominal values | 2° |

2.b | [0/90]_{s} |

2.c | [0/90]_{2} |

**Table 3.**
Case studies with uncertain ply thicknesses $({\mathrm{h}}_{\mathrm{ply}})$.

**Table 3.**
Case studies with uncertain ply thicknesses $({\mathrm{h}}_{\mathrm{ply}})$.

Case | $\mathbf{a}\mathbf{/}\mathbf{h}$ | Stacking Sequence | ${\mathsf{\mu}}_{{\mathbf{h}}_{\mathbf{p}\mathbf{l}\mathbf{y}}}$ | $\mathbf{C}\mathbf{o}{\mathbf{V}}_{{\mathbf{h}}_{\mathbf{p}\mathbf{l}\mathbf{y}}}$ |
---|

3.a | 20 | [0]_{4} | 0.131 mm | 7.5% |

3.b | [0/90]_{s} |

3.c | [0/90]_{2} |

4.a | 100 | [0]_{4} | 0.131 mm | 7.5% |

4.b | [0/90]_{s} |

4.c | [0/90]_{2} |

**Table 4.**
Correlation coefficients obtained with uncertain stacking angles for Case 1.a (left) and Case 2.a (right).

**Table 4.**
Correlation coefficients obtained with uncertain stacking angles for Case 1.a (left) and Case 2.a (right).

**θ**_{all} | 0.12 | −0.23 | 0.01 | **0.33** | **θ**_{all} | 0.16 | 0.18 | −0.07 | **0.35** |

| **θ**_{1} | −0.13 | −0.01 | −0.12 | | **θ**_{1} | 0.26 | −0.09 | −0.12 |

| | **θ**_{2} | −0.22 | −0.04 | | | **θ**_{2} | −0.18 | 0.04 |

**[0]**_{4} | | **θ**_{3} | −0.02 | | **[0]**_{4} | | **θ**_{3} | −0.05 |

$\mathbf{a}\mathbf{/}\mathbf{h}\mathbf{=}\mathbf{20}$ | | | **θ**_{4} | $\mathbf{a}\mathbf{/}\mathbf{h}\mathbf{=}\mathbf{100}$ | | | **θ**_{4} |

**Table 5.**
Correlation coefficients obtained with uncertain stacking angles for Case 1.b (left) and Case 2.b (right).

**Table 5.**
Correlation coefficients obtained with uncertain stacking angles for Case 1.b (left) and Case 2.b (right).

**θ**_{all} | **0.31** | 0.17 | **0.33** | **0.46** | **θ**_{all} | **0.32** | 0.14 | **0.33** | **0.49** |

| **θ**_{1} | 0.17 | 0.29 | −0.12 | | **θ**_{1} | 0.16 | 0.29 | −0.12 |

| | **θ**_{2} | −0.15 | −0.28 | | | **θ**_{2} | −0.15 | −0.27 |

**[0/90]s** | | **θ**_{3} | 0.27 | | **[0/90]s** | | **θ**_{3} | 0.27 |

$\mathbf{a}\mathbf{/}\mathbf{h}\mathbf{=}\mathbf{20}$ | | | **θ**_{4} | $\mathbf{a}\mathbf{/}\mathbf{h}\mathbf{=}\mathbf{100}$ | | | **θ**_{4} |

**Table 6.**
Correlation coefficients obtained with uncertain stacking angles for Case 1.c (left) and Case 2.c (right).

**Table 6.**
Correlation coefficients obtained with uncertain stacking angles for Case 1.c (left) and Case 2.c (right).

**θ**_{all} | **0.35** | 0.00 | −0.10 | **0.33** | **θ**_{all} | **0.36** | −0.01 | −0.09 | **0.33** |

| **θ**_{1} | 0.00 | 0.26 | −0.13 | | **θ**_{1} | 0.00 | 0.26 | −0.13 |

| | **θ**_{2} | −0.19 | 0.19 | | | **θ**_{2} | −0.20 | 0.19 |

**[0/90]**_{2} | | **θ**_{3} | −0.19 | | **[0/90]**_{2} | | **θ**_{3} | −0.20 |

$\mathbf{a}\mathbf{/}\mathbf{h}\mathbf{=}\mathbf{20}$ | | | **θ**_{4} | $\mathbf{a}\mathbf{/}\mathbf{h}\mathbf{=}\mathbf{100}$ | | | **θ**_{4} |

**Table 7.**
Correlation coefficients obtained with uncertain ply thicknesses for Case 3.a (left) and Case 4.a (right).

**Table 7.**
Correlation coefficients obtained with uncertain ply thicknesses for Case 3.a (left) and Case 4.a (right).

**h**_{all} | 0.10 | 0.17 | 0.24 | **0.97** | **h**_{all} | 0.10 | 0.17 | 0.24 | **0.97** |

| **h**_{1} | −0.01 | −0.01 | 0.02 | | **h**_{1} | −0.01 | −0.01 | 0.02 |

| | **h**_{2} | 0.04 | 0.09 | | | **h**_{2} | 0.04 | 0.10 |

**[0]**_{4} | | **h**_{3} | 0.02 | | **[0]**_{4} | | **h**_{3} | 0.02 |

$\mathbf{a}\mathbf{/}\mathbf{h}\mathbf{=}\mathbf{20}$ | | | **h**_{4} | $\mathbf{a}\mathbf{/}\mathbf{h}\mathbf{=}\mathbf{100}$ | | | **h**_{4} |

**Table 8.**
Correlation coefficients obtained with uncertain ply thicknesses for Case 3.b (left) and Case 4.b (right).

**Table 8.**
Correlation coefficients obtained with uncertain ply thicknesses for Case 3.b (left) and Case 4.b (right).

**h**_{all} | 0.06 | 0.25 | **0.45** | **0.88** | **h**_{all} | 0.06 | 0.26 | **0.45** | **0.88** |

| **h**_{1} | −0.02 | 0.00 | 0.02 | | **h**_{1} | −0.02 | 0.00 | 0.02 |

| | **h**_{2} | 0.05 | 0.10 | | | **h**_{2} | 0.05 | 0.10 |

**[0/90]**_{S} | | **h**_{3} | 0.01 | | **[0/90]**_{S} | | **h**_{3} | 0.01 |

$\mathbf{a}\mathbf{/}\mathbf{h}\mathbf{=}\mathbf{20}$ | | | **h**_{4} | $\mathbf{a}\mathbf{/}\mathbf{h}\mathbf{=}\mathbf{100}$ | | | **h**_{4} |

**Table 9.**
Correlation coefficients obtained with uncertain ply thicknesses for Case 3.c (left) and Case 4.c (right).

**Table 9.**
Correlation coefficients obtained with uncertain ply thicknesses for Case 3.c (left) and Case 4.c (right).

**h**_{all} | 0.10 | 0.18 | 0.24 | **0.97** | **h**_{all} | 0.09 | 0.18 | 0.22 | **0.97** |

| **h**_{1} | −0.01 | 0.00 | 0.02 | | **h**_{1} | −0.01 | 0.00 | 0.02 |

| | **h**_{2} | 0.05 | 0.10 | | | **h**_{2} | 0.05 | 0.10 |

**[0/90]**_{2} | | **h**_{3} | 0.02 | | **[0/90]**_{2} | | **h**_{3} | 0.02 |

$\mathbf{a}\mathbf{/}\mathbf{h}\mathbf{=}\mathbf{20}$ | | | **h**_{4} | $\mathbf{a}\mathbf{/}\mathbf{h}\mathbf{=}\mathbf{100}$ | | | **h**_{4} |

**Table 10.**
Multivariable linear regression models—initial case summaries.

**Table 10.**
Multivariable linear regression models—initial case summaries.

| ${\mathbf{w}}_{\mathbf{m}\mathbf{a}\mathbf{x}}$ | ${\mathbf{f}}_{\mathbf{1}}$ |
---|

Adj. ${\mathbf{R}}^{\mathbf{2}}$ | 97.44% | 99.77% |
---|

Model | F-test | p-value | F-test | p-value |

158.4 | <2.2 × 10^{−16} | 1543 | <2.2 × 10^{−16} |

| Estimate | p-value | Estimate | p-value |

$\mathsf{\beta}0$ | −5.856 × 10^{−4} | 3.67 × 10^{−15} *** | −6.162 × 10^{−1} | 0.07120 . |

$\mathsf{\beta}1$ | 5.492 × 10^{−16} | 2.96 × 10^{−8} *** | 2.626 × 10^{−11} | <2 × 10^{−16} *** |

$\mathsf{\beta}2$ | 9.294 × 10^{−16} | 0.3557 | 5.999 × 10^{−11} | 4.47 × 10^{−6} *** |

$\mathsf{\beta}3$ | 9.081 × 10^{−5} | 0.0165 * | 6.774 × 10^{−1} | 0.06491 . |

$\mathsf{\beta}4$ | −1.723 × 10^{−15} | 0.4396 | 1.974 × 10^{−11} | 0.37622 |

$\mathsf{\beta}5$ | −5.241 × 10^{−16} | 0.8048 | 7.866 × 10^{−11} | 0.00111 ** |

$\mathsf{\beta}6$ | −4.662 × 10^{−1} | 0.0822 . | 3.407 × 10^{−11} | 0.19487 |

$\mathsf{\beta}7$ | 1.829 × 10^{−1} | <2 × 10^{−16} *** | 5.360 × 10^{3} | <2 × 10^{−16} *** |

$\mathsf{\beta}8$ | - | - | −3.563 × 10^{−3} | <2 × 10^{−16} *** |

Residuals | Independence/normality rejected | OK |

**Table 11.**
Multivariable linear regression models—simplified case summaries.

**Table 11.**
Multivariable linear regression models—simplified case summaries.

| ${\mathbf{w}}_{\mathbf{m}\mathbf{a}\mathbf{x}}$ | ${\mathbf{f}}_{\mathbf{1}}$ |
---|

Adj. ${\mathbf{R}}^{\mathbf{2}}$ | 90.46% | 99.317% |
---|

Model | F-test | p-value | F-test | p-value |

276.1 | 4.917 × 10^{−16} | 1401 | <2.2 × 10^{−16} |

| Estimate | p-value | Estimate | p-value |

$\mathsf{\beta}0$ | −4.829 × 10^{−4} | <2 × 10^{−16} *** | 1.028 | 0.00254 ** |

$\mathsf{\beta}1$ | - | - | 2.606 × 10^{−11} | <2 × 10^{−16} *** |

$\mathsf{\beta}7$ | 1.806 × 10^{−1} | 4.92 × 10^{−16} *** | 5.343 × 10^{3} | <2 × 10^{−16} *** |

$\mathsf{\beta}8$ | - | - | −3.586 × 10^{−3} | <2 × 10^{−16} *** |

Residuals | OK | OK |