Ultimate limit state-based multi-objective optimum design technology for hull structural scantlings of merchant cargo ships
Introduction
A number of challenges are evident in today's industry practices of ship structural design. In many cases, the scantlings of structural members are not fully optimized. Some members are too strong, and others are either too weak or barely strong enough. It is obvious that both weight minimization and safety maximization should be achieved simultaneously, and that the strength requirements must be met. The current industry practices take more man-hours for the design process, because they are not fully automated. Design errors are often found in the later stages of the design, and some errors remain undiscovered until the construction is complete, as the design work is primarily based on manual labor.
It is therefore advisable to fully automate the design process. An automated procedure is obviously beneficial, not only for minimizing the structural weight, but also for maximizing structural safety. The man-hours required for design work can be decreased, and design errors can be avoided. In fact, the benefits of full optimization technology for structural design have already been realized for naval ships, for which it is critical to design structural weight in association with the functional requirements of armament. It is certainly time for the merchant shipbuilding industry to adopt this technology, as cost reduction is now a major challenge in a difficult global economy.
Many useful contributions are available in the literature toward the development of full optimization technologies for ship structural design. Hughes (1983) is a pioneer of the rationally based structural design of ships, in which full optimization is applied to determine the best design variables to meet the strength requirements and minimize the structural weight. Hughes and Paik (2013) further advance the methods for determining load and strength requirements within the framework of the structural design, in association with the ultimate limit states of plate panels, support members and hull girders. McNatt et al. (2013) develop multi-objective optimization techniques, and they implement all of their proposed technologies into a practical ship structural design tool named MAESTRO (2016). This tool involves a computer code that is useful for the finite element modeling of an entire ship, or a partial ship. MARSTRO can perform finite element analysis, evaluate limit states and optimize structural features with the use of designer-specified objective functions.
Zanic (2013) and Zanic et al. (2013) develop design support methodology that is applicable for multi-criteria synthesis in the design of practical, complex ship structures. An efficient design procedure is developed that is capable of solving design problems with multiple objectives. A design support system combines an efficient model for analysis, evaluation and design-related objective decision-making by using modules that are available in MAESTRO and OCTOPUS (2012).
Turkmen and Turan (2007) proposes an integrated optimization method that incorporates a multi-criteria decision-making algorithm. This method includes a technique for indicating designer preferences by their similarity to ideal solutions (Hwang and Yoon, 1981), a multi-objective genetic algorithm and a fast elitist non-dominated sorting genetic algorithm (Deb et al., 2000). The integrated optimization method is validated through its application to a Ro-Ro passenger ship design. Yang et al. (2014) propose a knowledge-based engineering methodology for structural optimization design. This method re-uses domain knowledge in a new design, and provides rational advice for increasing the design efficiency due to improvements in the workflow of ship design. Pedersen et al. (2013) proposes a systematic domain-independent method to design complex structures based on their hierarchical organization. This method enables effective and efficient design, numerical taxonomy to identify patterns of similarity in existing designs, technology diffusion to evaluate design processes, and multi-objective decisions regarding structures, design process, operational performance and cost.
A number of structural optimization technologies are also available that are based on design rules, such as the classification society's rules or the common structural rules (CSR) (IACS, 2012). Shin et al. (2006) propose a multi-objective optimization technique that follows one of the stochastic search methods. This technique identifies evaluation strategies, and applies them for the optimum design of CSR-based tankers, with consideration of the required freight rate. Payer and Schellin (2013) elaborates the classification society's rules in terms of rationally based ship structural design, as applied to the load calculation and analysis of large container ships under global hull girder loads, impact loads and high-frequency hull girder loads. Na and Karr (2013) develops an efficient stiffness method for using three-dimensional beam modeling, based on consideration of the span point and the eccentric system line. The purpose of this method is to reduce the computing time required for analysis, and yet provide sufficient accuracy of results in the CSR-based ship optimization design stage.
Most of the contributions in the literature are related to the efforts to optimize simplified structures such as a 2-dimensional hull girder cross section or very coarse mesh finite element models. However, the real structural system is very complex in geometry and it is then partitioned into subsystems, the subsystems are further portioned into components, the components into parts, and so on. Such complex structures must be modelled using thousands nodes and elements that are corresponding to the structural design variables of the optimization (Ma and Hughes, 2011; Ma et al., 2014; Ma et al., 2016). An efficient and accurate approach is then needed to achieve the optimization of such a structure with complexity.
In this paper, a full optimization procedure for the structural design of merchant cargo ships is developed using plate-shell finite element models. Multiple objectives are considered, including the minimization of structural weight and the maximization of structural safety. Ultimate limit states of the plate panels, support members and hull girders are applied in terms of the strength criteria associated with design constraints. As the process confirms that the design rules, e.g., the CSR, are satisfied, the design can gain approval by the classification societies.
The developed procedure is then applied to an as-built very large crude oil carrier (VLCC) class double hull oil tanker, and a comparison is made between the resulting design and the as-built reference ship. This comparison confirms the benefits of the developed methodology in terms of structural weight saving, structural safety improvement and savings in man-hour costs.
Section snippets
The current industry practice versus the developed procedure
An overview of the current industry practices for preliminary hull structural design is illustrated in Fig. 1. The strength and acceptable safety of ship structures at both the member and the global hull girder levels are quantified through application of the prescriptive and the design verification requirements for a strength assessment that uses finite element analysis. The design procedure starts with the target structure of one central cargo hold (using a three-hold model), and then the
Design variables and multi-objective functions
In the optimization process, the design variables can be the scantlings of longitudinal plate panels, the longitudinal stiffeners or the primary support members, such as the longitudinal girders and transverse frames shown in Fig. 4. The spacing of the longitudinal stiffeners and primary support members can also be design variables. In reality, the spacing of support members is fixed in advance, as per the requirements of cargo configuration and capacity. The actual optimization is usually
Extent of the analysis
The developed procedure can accommodate two options in terms of finite element modeling, as mentioned in Chapter 2. The first option is to perform the structural optimization for all three cargo holds at the same time, i.e., the mid-ship, aft and forward cargo hold regions. This approach requires making a structural model of the entire ship. For the best results, the optimization should be performed using an entire ship model.
The second option for making a three-cargo-hold model is to perform
Partial safety factor-based design criterion
As safety is one of the main design constraints in rationally based structural design, the safety of the structures is formulated in terms of partial safety factors. This formulation accounts for all of the uncertainties that affect the determination of the design variables, and the values of these uncertainties are based on the results of load effect analysis.
Partial safety factors are essential to enable accounting for different levels of safety and the degrees of seriousness of each
Optimization scheme for multi-objective functions
For structural optimization of the structural members, the first task is to identify the evaluation panels, which are the subjects of the ultimate strength evaluation, and the design clusters that are used to facilitate the structural manufacture process. Evaluation panels are collections of finite elements, which can be evaluated for their ultimate strength by using semi-analytical methods. The design cluster is any group of panels or grillages for which uniform design variables are desired,
Target ship – VLCC-class double hull oil tanker
The developed methodology is applied to the preliminary hull structural design of a VLCC-class double hull oil tanker. This ship consists of five cargo tanks, and a mid-ship cargo tank, the no. 3 hold, is selected as the target hold, as shown in Fig. 17. This ship's main particulars are given in Table 4, and mid-section structural profile is as shown in Fig. 18. The one cargo hold of 51.21 m has 3 separated cargo tanks with 2 oil-tight longitudinal bulkheads and 8 web frames, with a cross-tie
Concluding remarks
In this paper, a full optimization procedure for the structural design of merchant cargo ships is developed, and is shown to yield many benefits. Multiple objectives can be met with this procedure. Specifically, the minimization of structural weight and the maximization of structural safety can be achieved simultaneously. Due to the automated structural scantling process, considerable reductions can be achieved in the time required for design and in labor costs. These improvements can enable
Acknowledgements
This study was undertaken at the Lloyd's Register Foundation Research Centre of Excellence at Pusan National University, Busan, Korea. Lloyd's Register Foundation (LRF), a UK registered charity and sole shareholder of Lloyd's Register Group Ltd, invests in science, engineering and technology for public benefit, worldwide.
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