# Risk-Based Hybrid Light-Weight Ship Structural Design Accounting for Carbon Footprint
## 3 Hybrid Light-Weight Structural Design  
A novel ship structural design solution has been developed in [12] for a midship section design of a bulk carrier, where a part of the steel plates of the cargo holds was replaced by aluminium honeycomb sandwich panels creating a hybrid structure. The best design solutions for steel and hybrid use of steel and aluminium honeycomb panels were identified through the multiple criteria decision-making approach, demonstrating reduced ship costs and improved energy efficiency. The ship structural design was defined as a multi-objective optimisation problem with several objective functions, including minimum lightweight, minimum total ship cost as a function of the capital, operational and dismantling expenditures, minimum transportation cost, maximum transported cargo, and ultimate strength of the ship hull structure. The decision variables cover plate thickness, stiffener net-sectional area, shipbuilding yield stress, span and space and the constraints for the steel part of the ship hull structure are related to the plate thickness (local strength), section modulus (longitudinal strength) and critical buckling stress. The constraints for the AHS part of the ship hull are related to deflection, facing skin stress, shear stress in the core, panel buckling, shear crimping, skin wrinkling, intracell buckling and buckling. The descriptors of ship design solutions are given [11]. The ship length of the analysed ship is 224.5 m, the breadth is 40.7 m, the depth is 20 m, the block coefficient is 0.85, and the ship speed is 13 knots. For Steel, AHS1, and AHS2 design solutions, the draft is 14.60, 14.60 and 14.36 m, respectively, where the displacements are 116,227, 116,227, 114,342 tonnes, the cargo deadweights are 84,840, 100,489 and 98,625 tonnes. The lightweights are 16,107, 14,268 and 14,262 tonnes; the annual cargos are 776,604, 834,469 and 828,146 tonnes. The transportation cost for the three design solutions is 8.49, 7.31 and 7.35 \(\upxi\), where the ship cost is 20,717,152\(\upxi\), 18,721,159\(\upxi\) and 18,683,008\(\upxi\) and the attained EEDIs are 2.78, 2.76 and 2.75 g CO\({}_{2}\)/t-n m respectively. The bending-moment curvature relationship and the ultimate strength, defined as the maximum point of the hogging and sagging loading condition of the designed midship section subjected to vertical bending moments, are presented in Figure 2. The ultimate strength in sagging will be used as an input variable in the reliability analysis. The three analysed design solutions are designed to have the same initial ultimate strength. The AHS2 design solution, due to its less lightweight, shows a less draft, less transportation cost, less needed engine power, less attained energy efficiency design index (EEDI) [20,30] and less ship cost than the steel design solution. However, the AHS1 design solution uses the reduced lightweight to increase the deadweight and annual transported cargo for the same draft as steel design solutions and almost the same ship cost as the AHS2 design solution. Additionally, AHS 1 and AHS2 design solutions, due to the aluminium honeycomb panels, have a better corrosion degradation resistance. The corrosion degradation is accounted for by employing the non-linear time-dependent model developed in [31], where any corrosion-dependent variable is defined as:  
\[x_{i}=\left\{ \begin{array}{ll}x_{i,0}exp\left[-\frac{(t-\tau_{\text{C}})}{ \tau_{\text{I}}}\right],&t>\tau_{\text{C}}\\ x_{0},&t\leq\tau_{\text{C}}\end{array} \right. \tag{1}\]  
where \(x_{i,0}\) is the non-corroded status of variable \(x_{i}\), \(\tau_{\text{C}}\) is the coating life, and \(\tau_{\text{I}}\) is the transition life of the corrosion degradation process. The coating life and transition time for the steel design solution are 5 and 4 years, and for AHS 1 and AHS2, they are 5 and 7.12 years and 5 and 6.11 years, respectively. The coating life is assumed to be the same for the three design solutions.