Reliability-Based Optimal Design of Steel Box Structures. II: Ship Structure Applications

Traditional design of ship structures relies on a combination of experience, sound judgment, and deterministic approaches and typically ignores the potential for design improvement and other benefits offered through the use of reliability methods and structural optimization strategies. Part I of this article outlines the underlying theories involved in incorporating reliability methods and structural optimization strategies into the initial design of ship structures, whereas Part II (this paper) discusses their application to two case studies, namely, (1) a simple ship structure and (2) a more complex ship structure in an attempt to achieve weight reduction in the face of constraints on ultimate strength and buckling capacity. Using the approach outlined in the companion paper, a weight reduction of 5.6% was realized in the case of the simple vessel, whereas a 2.0% reduction was achieved in the case of the more complex vessel. A reduction in weight reduction has the potential to minimize the lifecycle cost, especially when including construction and operational and maintenance cost. These results highlight the potential benefits of reliability methods and structural optimization strategies, and encourage their implementation during the initial ship structural design phase. DOI: 10.1061/AJRUA6.0000830. © 2015 American Society of Civil Engineers. Author keywords: Reliability; Structural optimization; Ship structural design; Weight reduction. Introduction and Motivation Traditional design of ship structures has relied on a combination of engineering experience, sound judgment, and deterministic approaches, which effectively ignores many of the uncertainties inherent in structural design loads and capacities. These strategies have failed to incorporate advances in the areas of reliability methods and structural optimization (Kamat 1991). Part I of this twopart article reviews the theory involved with applying reliability methods and structural optimization to the initial design of ship hull structures, whereas Part II outlines the application of this theory to two ship structures: (1) a simple hull cross section and (2) a more complex ship hull titled “Energy Concentration.” In each case study, the objective of the analysis is to minimize weight, while ensuring that deterministicand reliability-based constraints on ultimate moment and buckling capacities are satisfied. This demonstration will closely follow the format presented in the companion paper (Part I). The results of each case study are shown to validate the accuracy of the strength models with previously documented analytical results. Simple Ship Structure Selection of Initial Design The initial design, taken from Mansour et al. (1997), is characterized by the principal dimensions shown in Fig. 1. Extra stiffeners are added to illustrate the concept of optimizing secondary stiffeners. The structure is constructed from steel, with a Young’s modulus of 206,000 MPa, a density of 7.85 × 10−9 N · s=mm, and a Poisson’s ratio of 0.30. The yield strength of the bottom and deck is 217.3 MPa, whereas that of the side shells is 276.5 MPa. The Caldwell, modified Caldwell, Paik, and elastic strength models (Ayyub et al. 2015) were used to compute the ultimate strength of the initial design. Table 1 shows the results. It is noted from the strength analysis that the elastic strength model produces the lowest moment capacity, whereas the Caldwell model, which employs a totally plastic approach, produces the highest moment capacity. Table 2 shows the ultimate buckling capacities. A knockdown factor of 0.92 was used in the elastic strength model to account for buckling. The initial weight (per unit length/g) of the structure is 0.24179 × 10−3 N · s=mm. This is currently an acceptable design and will be optimized using the methodology presented by Ayyub et al. (2015). Deterministic-Based Optimization of Initial Configuration Definition of Design Variables Some structural parameters, including plate thicknesses and stiffeners whose scantlings can be modified from those of the original design, are chosen as the design variables (Fig. 2 and Table 3). The current dimensions of the structural parameters constitute the initial design. To reflect practical realities, some parameters may be grouped and adjusted simultaneously in the design process. For example, a group may consist of a plate and three primary stiffeners. This group will be considered to have five design variables, i.e., plate thickness, web height, web thickness, flange width, and flange thickness, which are adjusted simultaneously in the Senior Risk Engineer, Reliability and Risk Team, Lloyd’s Register Martec, Suite 400, 1888 Brunswick St., Halifax, NS, Canada B3J 3J8 (corresponding author). E-mail: [email protected] Team Leader, Reliability and Risk Team, Lloyd’s Register Martec, Suite 400, 1888 Brunswick St., Halifax, NS, Canada B3J 3J8. Professor and Director, Center for Technology and Systems Management, Univ. of Maryland, College Park, MD 20742. Senior Research Engineer, Field Services and Trident Team, Lloyd’s Register Martec, Suite 400, 1888 Brunswick St., Halifax, NS, Canada B3J 3J8. Note. This manuscript was submitted on November 18, 2014; approved on April 14, 2015; published online on June 10, 2015. Discussion period open until November 10, 2015; separate discussions must be submitted for individual papers. This paper is part of the ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, © ASCE, 04015010(8)/$25.00. © ASCE 04015010-1 ASCE-ASME J. Risk Uncertainty Eng. Syst., Part A: Civ. Eng. ASCE-ASME J. Risk Uncertainty Eng. Syst., Part A: Civ. Eng. D ow nl oa de d fr om a sc el ib ra ry .o rg b y B ila l A yy ub o n 06 /1 4/ 15 . C op yr ig ht A SC E . F or p er so na l u se o nl y; a ll ri gh ts r es er ve d.