• Steel and Composite Structures
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• v.26 no.2
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• pp.163-170
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• 2018

The purpose of this paper is to present a new and efficient optimization algorithm called Jaya for optimum design of steel grillage structure. Constrained size optimization of this type of structure based on the LRFD-AISC is carried out with integer design variables by using cross-sectional area of W-shapes. The objective function of the problem is to find minimum weight of the grillage structure. The maximum stress ratio and the maximum displacement in the inner point of steel grillage structure are taken as the constraint for this optimization problem. To calculate the moment and shear force of the each member and calculate the joint displacement, the finite elements analysis is used. The developed computer program for the analysis and design of grillage structure and the optimization algorithm for Jaya are coded in MATLAB. The results obtained from this study are compared with the previous works for grillage structure. The results show that the Jaya algorithm presented in this study can be effectively used in the optimal design of grillage structures.

• Journal of the Society of Naval Architects of Korea
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• v.59 no.1
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• pp.39-45
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• 2022

Normal strategy of structure optimization procedure has been minimum cost or weight design. Minimum weight design satisfying an allowable stress has been used for the ship and offshore structure, but minimum cost design could be used for the case of high human cost. Natural frequency analysis and forced vibration one have been used for the strength estimation of marine structures. For the case of high precision experiment facilities in marine field, the structure has normally enough margin in allowable stress aspect and sometimes needs high natural frequency of structure to obtain very high precise experiment results. It is not easy to obtain a structure design with high natural frequency, since the natural frequency depend on the stiffness to mass ratio of the structure and increase of structural stiffness ordinary accompanies the increase of mass. It is further difficult at the grillage structure design using the profiles, because the properties of profiles are not continuous but discrete, and resource of profiles are limited at the design of grillage structure. In this paper, the grillage structure design system under the constraint of high natural frequency is introduced. The design system adopted genetic algorithm to realize optimization procedure and can be used at the design of the experimental facilities of marine field such as a towing carriage, PMM, test frame, measuring frame and rotating arm.

• Journal of Navigation and Port Research
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• v.30 no.2
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• pp.137-143
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• 2006

The optimum grillage design belongs to nonlinear constrained optimization problem. The determination of beam scantlings for the grillage structure is a very crucial matter out of whole structural design process. The performance of optimization methods, based on penalty functions, is highly problem-dependent and many methods require additional tuning of some variables. This additional tuning is the influences of penalty coefficient, which depend strongly on the degree of constraint violation. Moreover, Binary-coded Genetic Algorithm (BGA) meets certain difficulties when dealing with continuous and/or discrete search spaces with large dimensions. With the above reasons, Real-coded Micro-Genetic Algorithm ($R{\mu}GA$) is proposed to find the optimum beam scantlings of the grillage structure without handling any of penalty functions. $R{\mu}GA$ can help in avoiding the premature convergence and search for global solution-spaces, because of its wide spread applicability, global perspective and inherent parallelism. Direct stiffness method is used as a numerical tool for the grillage analysis. In optimization study to find minimum weight, sensitivity study is carried out with varying beam configurations. From the simulation results, it has been concluded that the proposed $R{\mu}GA$ is an effective optimization tool for solving continuous and/or discrete nonlinear real-world optimization problems.

• Bulletin of the Society of Naval Architects of Korea
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• v.25 no.1
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• pp.11-20
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• 1988

From the engineering point of view, a synthesis as well as an analysis technique is explored to search for the improved design of grillage which is common in ship structure. As an approximate analysis method for the grillage, an interaction reaction method is developed and compared with the finite element method. It is found that the discrepancy between these two methods is so negligible that the percent method could be used effectively for the grillage analysis. As an optimization technique, a feasible direction method could be used is combined with the intersection reaction method in order to design a minimum weight optimal grillage. The feasible direction method shows a good numerical performance although it requires more calculation times compared with the direct search method. Finally, the application of multiple objective optimization method to grillage is investigated in order to resolve conflicts existed between the multiple objectives which is a common characteristic of structure design problem. Goal programming method is extended to handle a nonlinear property of constraints and objective functions. It seems that the nonlinear goal programming could help not only to establish a relative importance of each objective, but also enable the designer to choose the best combination of design variables.

• Structural Engineering and Mechanics
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• v.31 no.2
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• pp.137-152
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• 2009

Mechanic behavior of Y-shape thin-walled box girder bridge structure is complex, so one can not exactly hold the mechanical behavior of the Y-shape thin-walled box girder bridge structure through general calculation theory and analytical method. To hold the mechanical behavior better, based on elementary beam theory, by increasing the degree of freedom analytical method, taking account of restrained torsiondistortion angledistortion warp and shearing lag effect at the same time, authors obtain a thin-walled box beam analytical element of 10 degrees of freedom of every node, derive stiffness matrix of the element, and code a finite element procedure. In addition, authors combine the obtained procedure with spatial grillage analytical method, meanwhile, they build a new analytical method that is the spatial thin-walled box girder element grillage analysis method. In order to validate the precision of the obtained analysis method, authors analyze a type Y-shape thin-walled box girder bridge structure according to the elementary beam theory analytical method, the shell theory analytical method and the spatial thin-walled box girder element grillage analysis method respectively. At last, authors test a type Y-shape thin-walled box girder bridge structure. Comparisons of the results of theory analysis with the experimental text show that the spatial thin-walled box girder element grillage analysis method is simple and exact. The research results are helpful for the knowledge of the mechanics property of these Y-shape thin-walled box girder bridge structures.

• Journal of the Society of Naval Architects of Korea
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• v.45 no.6
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• pp.710-718
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• 2008

This paper presents a simple and fast approach to plan the arrangement of supports and to do a ship docking analysis. The unpredicted structural damages often happen from a docking works as the size of ships are getting larger and larger. In docking a ship, excessive reaction forces from supports are primary causes of the structural damage. The grillage analysis method is employed to simply calculate only the reaction forces at supports. The grillage modeling strategies are proposed to improve the accuracy. In this paper, the results obtained by the proposed approach are compared with those of the current whole-ship FEA for typical types of ships. Comparison shows that the results from the present grillage approaches are reasonably in a good agreement with the 3-D full F.E one. Finally, an integrated program developed for the ship docking analysis is described.

• Journal of the Society of Naval Architects of Korea
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• v.44 no.6
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• pp.605-611
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• 2007

A ship is composed of many grillage structures especially the deck which is consists of primary girders, transverse and longitudinal members. Several holes are arranged on these primary members for pipes, vents, etc. which cause stress concentration due to the discontinuity of the member. It is not easy to get the stress values around all these holes because of the huge amount of time necessary for computations. In this paper, a simple method to compute for the stress around the holes is suggested. This method is composed of two steps which are grillage analysis for primary members and detailed stress analysis using the results of the grillage analysis. This method is made for the design of the primary members with openings supporting the deck structure.

• Journal of the Korean Society of Industry Convergence
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• v.4 no.2
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• pp.157-166
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• 2001

The purpose of this study is to examine the accuracy of the code provisions on lateral load distribution factors of prestressed concrete girder bridges. Most designers in Korea use the lever method or lateral load distribution formula in the existing design codes. However, the methods do not account for the effect of bridge skew or direction of diaphragm. Therefore, this study analysed the prestressed concrete girder bridge with grillage model for various girder spacings, directions of diaphragms, span lengths, and skews, and compared the results with those of existing design code. It has been found that lateral load distribution factors were proportional to the girder spacing while they were not significantly affected by the change of span length, direction of diaphragm, and skew. For bending moments, lateral load distribution factors from the grillage analysis were 60%~68% of those from Korean bridge design code. Therefore, the code provisions result in very conservative design. For support reactions, however, lateral load distribution factors from the grillage analysis were slightly greater than those from Korean bridge design code. Therefore, the capacity of bearings of the bridge with a large skew should be determined by grillage analysis.

• Journal of the Korean Society of Marine Environment & Safety
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• v.19 no.3
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• pp.290-301
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• 2013

The docking analysis of a global ship structure is requested to evaluate its structural safety against the reaction forces at supports during docking works inside a dry dock. That problem becomes more important recently as the size of ships is getting larger and larger. The docking supports are appropriately arranged in a dock to avoid their excessive reaction forces which primarily cause the structural damages in docking a ship and, up to now, the structural safety has been assessed against the support arrangement by the finite element analysis (FEA) of a global ship structure. However, it is complicated to establish the finite element model of the ship in the current structural design environment of a shipyard and it takes over a month to finish the work. This paper investigates a simple and fast approach to carry out a ship docking analysis by a simplified grillage model and to assign the docking supports position on the model. The grillage analysis was considered from the motivation that only the reaction forces at supports are sufficient to assess their arrangement. Since the simplified grillage model of the ship cannot guarantee its accuracy quantitatively, modeling strategies are proposed to improve the accuracy. In this paper, comparisons between the proposed approach and three-dimensional FEA for typical types of ships show that the results from the present grillage model have reasonably good agreement with the FEA model. Finally, an integrated program developed for docking supports planning and its evaluation by the proposed approach is briefly described.

• Journal of the Korea institute for structural maintenance and inspection
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• v.9 no.1
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• pp.159-170
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• 2005

The grid structure is parallel main girders intersected with crossgirder. It distribute the loads to adjoining main girder through the crossgirder when a girder is subjected to a load. grillage girder bridge has high load-carrying capacity, it can save materials and become more economical type of bridge. In this paper, the grillage girder bridge analysis program developed by using the transfer matrix method deals with following problems: the comparision with Leonhardt, Szabo, FEM yang and jung in the analysis of grillage girder bridges, quality of straight and curved bridges with skew angle, forces of straight and curved bridges according to skew angle and bending stiffness/torsional stiffness ratio.