Journal of NUCLEAR SCIENCE and TECHNOLOGY, Vol. 40, No. 12, p. 989–997 (December 2003)
ORIGINAL PAPER
Design of a Spacer Grid Using Axiomatic Design Ki-Jong PARK1 , Byung-Soo KANG2 , Kee-Nam SONG3 and Gyung-Jin PARK4,* 1
Department of Machine Design and Production Engineering, Hanyang University, 1271 Sa-1 dong, Ansan, Kyunggi-do, 425-791, Korea 2 Center of Innovative Design Optimization Technology, 17 Haengdang-dong, Seongdong-gu, Seoul, 133-791, Korea 3 Korea Atomic Energy Research Institute, 150 Dukjin-dong, Yusong-gu, Taejon, 305-353, Korea 4 Division of Mechanical and Information Management Engineering, Hanyang University, 1271 Sa-1 dong, Ansan, Kyunggi-do, 425-791, Korea (Received March 3, 2003 and accepted in revised form July 30, 2003) Recently, much attention is focused on the design of fuel assemblies in the Pressurized Light Water Reactor (PWR). The spacer grid is one of the main structural components in a fuel assembly. It supports fuel rods, guides cooling water, and maintains geometry from external impact loads. In this research, a new shape of the spacer grid is designed by axiomatic approach. The Independence Axiom is utilized for the design. For the conceptual design, functional requirements (FRs) are defined and corresponding design parameters (DPs) are found to satisfy corresponding FRs in sequence. Overall configuration and shapes are determined in this process. Detailed design is carried out based on the sequence from axiomatic design. For the detailed design, the system performances are evaluated by using linear and nonlinear finite element analyses. The dimensions are determined by optimization. Some commercial codes are utilized for the analysis and design. KEYWORDS: axiomatic design, independence axiom, decoupled design, design parameter, functional requirement, impact load, shape optimization, contact pressure, PWR type reactors, nuclear fuel rod support grid
I. Introduction The nuclear fuel assembly in Fig. 1 is used in a PWR. It is composed of a top end piece, a bottom end piece, guide thimbles, fuel rods, and spacer grids. The slenderness ratio of the fuel rod is so high that several spacer grids need to support the rod in order to prevent its unstable structural behavior. The actual supporting parts in the spacer grid are the springs and dimples as illustrated in Fig. 2. Structural performance of these supporting parts is critical for stable support of the fuel rod.1–7) Moreover, in an abnormal operating environment such as in an earthquake, most of the external impact loads are mainly applied to the spacer grids supporting the fuel rods. Control rods normally reside outside of the spacer grids. Under an abnormal operating environment or when controlling the core power, control rods must be quickly inserted in the nuclear reaction zone through the guide thimbles that are fixed to spacer grids via sleeves or welding. Therefore, deformation of spacers needs to be limited to safely maintain the guide thimbles.8–11) The spacer design has to consider many complex engineering aspects such as structural aspects, metallurgy, thermalhydraulics, manufacturing limitations, etc. In this research, the design of a spacer grid is conducted from structural viewpoints. Other complex aspects are indirectly considered with the results of previous researches4–7) in the design process. The conceptual design process is proposed by the axiomatic approach.12–17) The proposed process is reasonable and systematic compared to the conventional design process based on experience and sophisticated analysis methods. Two axioms exist in axiomatic design. One is the Indepen∗
Corresponding author, Tel. +82-31-400-5246, Fax. +82-31-4070755, E-mail:
[email protected]
Fig. 1 Nuclear fuel assembly
dence Axiom and the other is the Information Axiom. The Independence Axiom is employed to design the spacer grid. After the conceptual design, detailed design is performed to solve each problem indicated by the design matrix of the axiomatic approach. The detailed design includes three structural analysis problems. They are evaluations of the inner strap strength using non-linear dynamic analysis, the contact behavior between the fuel rod and the grid spring using non-linear static analysis, and the strength of the grid spring arms using linear static analysis. The finite element method is adopted for the analyses.18) Some commercial software systems are utilized. LS-DYNA3D,19) an explicit dynamic analysis software system and ABAQUS/Standard20) an implicit analysis software system, are used for nonlinear dynamic analysis and nonlinear static contact analysis, respectively. To determine the final shape of the grid spring arms, numerical structural optimization is employed by using a commercial
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Figure 3 is a graphical interpretation of the general mapping process between the functional domains and physical domains. Consider the following design equation to understand the implications of the Independence Axiom: {FRs} = [A]{DPs},
Fig. 2 Unit spacer grid structure
software system called GENESIS21, 22) which is capable of structural optimization with linear static analysis.
II. Axiomatic Design15) Design is a continuous interplay between what to achieve and how to achieve it. The designer determines what to obtain by defining the design objectives from the Customer Attributes (CAs). The “what to achieve” items are the functional requirements (FRs). The answer to the question, “how to achieve them” is obtained by the definition of design parameters (DPs) in the physical domain. In the axiomatic approach, a design is the creation of the solutions that can obtain stated objectives through mapping from FRs to DPs through the proper selection of DPs that satisfy the FRs. Then, it is the obligation of the designer to select the appropriate FRs and their corresponding DPs. If a completed design does not satisfy perceived needs or prescribed FRs, the designer must create a new idea to change the DPs or FRs. This process is repeated until the designer gets reasonable FRs and corresponding DPs. The Independence Axiom in axiomatic design suggests that one DP influences only a corresponding FR in the mapping process between the functional domain and the physical domain; i.e. it suggests one-to-one mapping of FRs and DPs.
(a) General process
(1)
where {FRs} is the vector of the functional requirements, {DPs} is the vector of the design parameter, and [A] is the design matrix that identifies the relationship between {FRs} and {DPs}. The design matrix consists of three types as follows: –Coupled design X X X DP1 FR1 FR2 = X X X DP2 , (2) DP3 FR3 X X X –Decoupled design X FR1 FR2 = X FR3 X
O X X
O DP1 O DP2 , X DP3
–Uncoupled design X FR1 FR2 = O FR3 O
O X O
O DP1 O DP2 , X DP3
(3)
(4)
where X means an FR and a DP have a certain relationship and O means they have no relationship. In Eq. (2), DP1, DP2, and DP3 are to be determined simultaneously to satisfy FR1. However, even though they satisfy FR1, they cannot be guaranteed to satisfy FR2 or FR3. Therefore, many trials and errors are needed to find the correct values of all DPs. It is possible to conduct a sequential design in the case of Eq. (3). That is, we can determine the design parameters in the sequence of DP1, DP2, and DP3. In Eq. (4), an FR corresponds exclusively to only one DP. A designer can treat one FR–DP set regardless of the remaining two FR–DP sets. Therefore, when a variation exists in a certain FR–DP set, there is no influence from the variation over the other FR–DP sets. That is, each FR is independent of the other FRs. The Independence Axiom recommends the uncoupled design as shown in Eq. (4). In this design, the relationship be-
(b) The hierarchy and zigzag mapping process for this research
Fig. 3 Concept of domain, mapping and decomposition JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY
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tween the FR and the DP is one-to-one. If it is impossible to achieve this design, the next best is a decoupled design as shown in Eq. (3). The coupled design in Eq. (2) is not desirable from the viewpoint of axiomatic design. In this case, the designer must create new ideas for FRs or DPs to achieve a decoupled design or an uncoupled design. The Information Axiom is used to select the best design out of several designs that satisfy the Independence Axiom. According to the Information Axiom, the best design among those satisfying the Independence Axiom is the one with the least information content. The axiomatic design research group says that the information content may be inversely proportional to the probability of achieving design goals. In this work, the design of a spacer grid is carried out by using only the Independence Axiom because multiple design candidates are not extracted. The FRs and DPs are decomposed to make a hierarchy and a zigzag mapping process is used during the decomposition.12–17) The process is illustrated in Fig. 3. The FRs for a design problem are decomposed into a hierarchy, and the total design description at any level of the hierarchy consists of the engineering aspects needed to satisfy the stated objectives. Thus, the FR–DP mapping process takes place over a number of levels of abstraction, but a given set of FRs must be successfully mapped to a set of DPs in the physical domain prior to the decomposition of the FRs. Iterations between FR-toDP mapping and functional decomposition need zigzagging processes between the functional and physical domains. Actually, when the hierarchy arrives at the bottom leaves, the design is completed.
III. Design of a Spacer Grid Using the Independence Axiom 1. Description of the Problem As mentioned earlier, the spacer grid in Fig. 2 is a part of the fuel assembly that supports the fuel rod. Here are the general features that a spacer grid must have.4–7) First, it must make the fuel rod stationary. Second, it must supply a cooling flow path that encourages heat transfer from the hot fuel rod to the coolant. Third, it must protect the control rod guide path in any abnormal operating environment. A designer needs to consider the above features in designing a spacer grid; the third feature, the design for consistent safe operation such as safe shutdown of the reactor in an emergency is especially important. The above general features are related to various complex engineering fields such as structural mechanics, metallurgy, thermal-hydraulics and manufacturing. In reality, it is extremely difficult to consider all the disciplines simultaneously even in modern engineering. Therefore, when a component is designed by using a certain discipline, data from other disciplines are generally assigned fixed values. By the same token, some values are fixed as constants from other disciplines4–7) or some aspects are ignored due to simplification of the model. For example, the finite element (FE) model utilized in this research is illustrated in Fig. 4 and it has 5 by 5 grids. Actually, the real full model has 16 by 16 grids. The simplified spacer assembly model without the thimble sleeve
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Fig. 4 Applied boundary condition for impact FE analysis model of 5 by 5 cell grid
and fuel rod is enough to grasp the design trend at the conceptual design stage because their effects are not large.4–7) Welding spots are modeled by merging the nodes and they are tuned by experiments. And several parameters such as strap thickness, material property, etc. are also not considered in the design process. These parameters have been determined from other disciplines such as structural mechanics and thermalhydraulics. Thus, this work is limited to those boundaries. In an abnormal operating environment such as in an earthquake, lateral impact loads are applied to the spacer grids as illustrated in Fig. 5. The spacer gird must protect the guide path of the control rod against these lateral impact loads. Therefore, the spacer grid must have sufficient strength against this load. A fuel rod contacts with the spring because the spring sup-
Fig. 5 Unit spacer grid under impact load
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Fig. 6 Contact between a nuclear fuel rod and a spring Fig. 7 Unit inner strap in a spacer grid without the spring
ports the fuel rod as illustrated in Fig. 6. Thus, there must be contact pressure on the contact surface. Flow induced vibration from the coolant also causes the fretting phenomenon, which results in wearing down of fuel rods and leakage of radioactive products. Therefore, wearing down of the fuel rod should be prevented. When a fuel rod is inserted into the spacer grid, most deformation occurs not in the dimple, but in the spring because the dimple is stiffer. Generally, the deformation behavior is elasto-plastic. The grid spring loses its strength due to irradiation-induced relaxation and creep-down of fuel rod diameter. Consideration must be made at the design stage to keep the supporting reaction force throughout the lifetime of the reactor. Therefore, plastic deformation in the spring must be minimized and the grid spring must support the fuel rod with the proper initial force. Based on these observations, FRs and DPs are defined from a zigzagging process and decomposition. 2. Conceptual Design by Definition of the Design Equation A spacer grid must have sufficient strength to protect the guide path of the control rod against lateral impact loads. The spacer grid assembly is composed of inner and outer straps, fuel rods, thimble sleeves, etc. As mentioned earlier, thimble sleeves and fuel rods have little influence on strength of the structure. Thus, they are not considered in the analysis and design process. Therefore, the main components responsible for the strength of the spacer grid are the outer and inner straps as illustrated in Fig. 5. The strength of the outer strap is mainly dependent on its thickness. But the thickness of the outer strap is fixed to 0.664 mm because the simplified model of 5 by 5 grid cells is used in this work. Actually, the outer strap is located around the edges of the 16 by 16 full model. Thus, we can only control the strength of the inner strap to resist the impact load. The main part of the inner strap which resists the impact load is illustrated in Fig. 7. Therefore, FR1 and DP1 are defined as follows: FR1: Control strength of the inner strap DP1: Dimension l in Fig. 7. The spacer grid must safely support the fuel rod. Thus, FR2 and DP2 are as follows: FR2: Support fuel rod safely DP2: Supporting part for the fuel rod (spring). The type of the design matrix is determined by the relation-
ship between FRs and DPs. In this work, the supporting part for the fuel rod is placed at the center of the inner strap as illustrated in Fig. 7. Therefore, after the strength of the inner strap (FR1) is determined, the space for the supporting part can be fixed. The design is a decoupled design as FR1 X O DP1 = . (5) FR2 X X DP2 The supporting part needs to prevent leaking of radioactivity caused by wearing due to contact pressure and the fretting phenomenon. Also, it needs to reduce the plastic deformation to maintain the required spring force. Thus FR2 is decomposed into the following two functional requirements: FR21: Reduce the contact pressure on the contact surface FR22: Reduce the maximum stress of spring under a specific spring force. Once the contact force is introduced, the contact pressure is determined by the contact area. Thus the contact area can control the contact pressure. The spring force and the strength of the spring are the result of the shape and thickness of the spring. The thickness of the spring cannot be designed due to restrictions in the manufacturing process. Thus the shape of the spring controls the spring force and the stress in the spring. Therefore, the above second level FRs are mapped to the following second level DPs: DP21: The shape of the contact part of the spring DP22: The shape of the spring arms. The fixed shape of the contact area of the spring imposes a small restriction on the shape change of the spring so that FR21 is hardly related to DP22. The design equation for the second level is as follows: FR21 X O DP21 = . (6) FR22 X X DP22 As design matrices in Eqs. (5) and (6) indicate, the spacer grid is designed in the sequence of DP1, DP21 and DP22. 3. Detailed Design of the Design Parameter Dimensionl Prior to decision of DP1, it is necessary to define the critical impact load of a spacer grid from experiments as follows. In an experiment, the magnitude of impact load is gradually increased and applied to a spacer grid. If the maximum reaction force of the spacer grid does not increase any more at the ith step, then the impact load applied at the (i−1)th step JOURNAL OF NUCLEAR SCIENCE AND TECHNOLOGY
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Fig. 8 Schematic diagram for free fall shock machine Table 1 Material properties of Zircaloy-4 Elastic
Plastic
E (GPa)
σy (MPa)
ρ (kg/m3 )
ν
σ (MPa)
ε
105.15
328.0
6,550
0.294
328.0 443.0
0.0 0.340
is considered as the critical impact load.10) First the dimension of l is determined so that the critical impact load of the designed spacer grid is higher than or equal to a nominal value. The nominal value can be obtained from an experiment with the existing spacer grids that are currently used in reactor. Experiments with existing ones have been carried out a few times to get the mean value of the critical impact load using the free-fall tester as illustrated in Fig. 8.18) Since the mean value of the critical impact load from the experiments is 4,500N, the nominal value of the critical impact load is set to 4,500N. For numerical simulation, the FE model in Fig. 4 is developed.19) The model has a rigid sphere with mass and initial velocity, a rigid plate and the spacer grid with shell elements for impact analysis. The impact load is obtained from the contact force among them. For higher velocity, larger impact load is developed. The target for this simulation is to find a value of l for the critical impact load with the nominal value of 4,500N. Material properties in Table 1 are used in the simulation. As a result of several nonlinear analyses with several candidate values of l, the critical impact load of a spacer grid with l of 4.374 mm is slightly higher than the nominal value. Therefore, the dimension of DP1 is determined to be 4.374 mm. 4. Detailed Design of the Shape of the Contact Area (DP21) and the Shape of the Spring (DP22) Due to the coolant flow, the fuel rod vibrates with the supports from the springs.5) The relative infinitesimal motion between two bodies causes fretting wear on the contact surfaces of the fuel rod and spring. A design should be performed to minimize the wear and it can be achieved through mini-
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Fig. 9 Contact pressure contour and contact area
Table 2 Contact pressure and area for DP21
Contact pressure (N/mm2 ) Contact area (mm2 )
Original design
Improved design
2,190.0 0.1126
323.0 0.8528
mization and uniform distribution of the local contact pressure (DP21). Improved shapes are searched through many trials and errors in simulation. The original shape and the final result are illustrated in Fig. 9 and Table 2. In the new design, the contact pressure is considerably reduced and the contact area is larger than that of the original design. Next, the shape of the spring (DP22) should be determined to minimize the maximum stress. The spring is deformed by the manufacturing tolerance of the fuel rod assembly, excessive shipping loads, and the loading condition in the nuclear reactor. The load applied to the spring in a spacer grid can be expressed by Eq. (7). Due to the radiation by neutrons in the reactor, only about 8% of the initial spring force remains after long-term operation. A load with about 2N from the fluid induced vibration is applied to the spring.9, 11) Therefore, to support the fuel rod throughout the operating period, the initial spring force of a spacer grid must be greater than 25N as shown in Eq. (8) which is a brief expression of Eq. (7): Fspring × 0.08 > 2N
(7)
Fspring > 25N after manufacturing of fuel assemblies. (8) After manufacturing of fuel assemblies, it has been found that the spring of the spacer grid was deformed by about 0.2 mm due to the insertion of the fuel rod through the spacer
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grid.9, 11) At that very moment, the supporting load of the spring is equivalent to Eq. (8). It is the initial supporting condition which the spring must have before operating the reactor. However, the fuel rod is pulled into each spacer grid cell and the maximum height difference among grid cells is 0.4 mm. The grid spring has the same deflection during the manufacturing process as illustrated in Fig. 10. The height difference is caused by manufacturing tolerances. After insertion of the rod, the performance of the grid spring can be deteriorated if the excessively deformed spring is not able to be recovered to the initial displacement of 0.2 mm with 25N. Generally speaking, considering the above deformation and height difference, a load of 50N is applied to a linear spring and the linear spring is deformed by 0.4 mm. That means the best spring in a spacer grid has the ideal behavior characteristics as illustrated in Fig. 11. However, most of the springs actually exhibit partial plastic deformation at the displacement of 0.4 mm. Thus, the spring can be nearly linear if the plastic
deformation is minimized in the above force-deflection range. It is noted that the design is a decoupled design as shown in Eq. (5). Thus DP1 fixes a space for the spring. Moreover, the shape of the contact part somewhat reduces the room for designing the shape of the spring as shown in Eq. (6). Under these circumstances, the problem is defined with the maximum stress as the objective function. The optimization problem is formulated for the spring shape DP22 as follows: Find
DP22
to minimize maximum stress subject to
[K ]{δ} = { f } δmax = 0.4 mm,
(9)
where [K ] is the stiffness matrix, {δ} is the displacement vector, { f } is the external force of the finite element analysis equation, and δmax is the deflection at the center of the spring. When a maximum property is included in the optimization formulation, the problem can be solved by using an artificial variable as follows:23) Find
DP22
to minimize β subject to
[K ]{δ} = { f } σ < β (at all the elements of FE analysis) δmax = 0.4 mm,
(10)
where β is the artificial variable. The artificial variable β is used for the objective function of a min-max problem. Thus, the artificial variable β is minimized while the constraints including all the stresses are satisfied. The shape of the spring obtained from this formulation minimizes the maximum stress subject to the displacement of 0.4 mm under the given constant load in the elastic range. For shape optimization,24, 25) a quarter FE model of the spring is utilized as illustrated in Fig. 12 and design variables are indicated in Fig. 13. DVx is the xth design variable in Fig. 13 and Table 3. That is, DP22 is a vector which consists of eleven design variables in Fig. 13. They are the changes of the coordinates on selected nodal points. Overall shape changes of the FE model can be obtained by interpolation or extrapolation between them.22) Fig. 10 Manufacturing process of fuel assembly and schematic diagram
Fig. 11 Ideal force–displacement curve for a grid spring
Fig. 12 Initial unit inner strap and its quarter model
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Design of a Spacer Grid Using Axiomatic Design Table 3 Results of optimization Design variable DV1 DV2 DV3 DV4 DV5 DV6 DV7 DV8 DV9 DV10 DV11
The changes of x-coordinate of node a in Fig. 13 The changes of x-coordinate of node b in Fig. 13 The changes of x-coordinate of node c in Fig. 13 The changes of x-coordinate of node d in Fig. 13 The changes of x-coordinate of node e in Fig. 13 The changes of x-coordinate of node g in Fig. 13 The changes of z-coordinate of nodes a and d in Fig. 13 The changes of y-coordinate of node a in Fig. 13 The changes of y-coordinate of node d in Fig. 13 The changes of x-coordinate of node f in Fig. 13 The changes of x-coordinate of node h in Fig. 13
Objective function
An artificial variable β
Initial design
Optimal design
0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0
6.0749 6.0749 15.0 −9.9988 −9.9988 −0.41806 3.2036 9.0000 3.7836 −9.9988 −0.41806
2.0
0.47936
Fig. 13 A quarter FE model and design variables
The problem in Eq. (10) is a nonlinear programming problem and solved by a structural optimization system named as GENESIS.18, 19) As mentioned earlier, since springs exhibit plastic deformation under the above loading condition, it is necessary to do a nonlinear analysis to consider plastic deformation. It is extremely difficult to directly consider nonlinear analysis in structural optimization. It is desirable to exploit the benefit of linear static optimization. Therefore, a design process is defined as illustrated in Fig. 14. The aim of this process is to achieve 50N reaction while the maximum stress is minimized under plastic deformation of 0.4 mm.9, 11) The given constant load in Eq. (9) is near 50N. The results of the optimization are shown in Table 3. The maximum stress exceeds the yield stress of 0.382 GPa. Because some plastic deformation is allowed, the design is considered acceptable. The design process gives the shape of the spring (DP22) as illustrated in Fig. 15.
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Fig. 14 Design process for DP22
Fig. 15 Designed unit inner strap
IV. Discussion Nonlinear dynamic analysis is done to evaluate the critical impact load of the designed spacer grid. Results of the
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a structural viewpoint. But the real working environment of spacer grids should be analyzed from various viewpoints such as thermodynamics, fluid dynamics, structural dynamics, and nuclear engineering. If these are considered, the functional requirements might be changed or even conflict with those from non-structural dynamics considerations. These days, multidisciplinary design optimization (MDO) is being developed to consider multiple disciplines in the optimization process. Therefore, it is necessary to employ an MDO method in future studies.
Acknowledgments
Fig. 16 Force–velocity curve of the designed spacer grid
vspace*-3pt
FE analysis are illustrated in Fig. 16. To save analysis time, two spacer grids are selected, without the spring illustrated in Fig. 7, and with the spring illustrated in Fig. 15. Compared to the spacer grid without the spring, the critical load of the product with the spring is slightly higher by 100N. Thus, it is not exactly true that the supporting part (DP2) does not affect the strength of the inner strap (FR1) as mentioned in Eq. (5). However, the influence of DP2 upon FR1 is sufficiently small. Therefore, the spring effect is considered to be negligible for the strength of the inner strap, and the design matrix is a decoupled one as shown Eq. (5). This consideration is backed up by a theorem which implies that if the amount of the effect by a DP on an FR is less than the designer specified tolerance in an element of design matrix, that element can be neglected.15) The design matrix of the spacer grid in this work is a decoupled one. Thus, if change is required for the strength of the inner strap, the shape of the spring should be redesigned. And if the loading condition of the spring is to be changed, only the shape of the spring can be changed, not the strength of the inner strap.
V. Conclusions A conceptual design process was proposed for a spacer grid using the Independence Axiom. Functional requirements were defined and mapped onto appropriate design parameters. A functional requirement of the first level was decomposed into two functional requirements of the second level. The design was found to be decoupled and detailed designs were carried out based on the sequences that the design equations indicated. In the detailed design, finite element analyses and numerical optimizations were employed. The performance of the new design was significantly improved. The research was conducted for a simplified model with 5 by 5 grids while the full model has 16 by 16 grids. Currently, design work with 16 by 16 grids is being performed with a larger number of design variables and the same method explained in this paper. The functional requirements in this work were defined from
This research was supported by the high performance spacer grid structure program of the Korea Atomic Energy Research Institute. This research was also supported by the Center of Innovative Design Optimization Technology, Korea Science and Engineering Foundation. The authors are thankful to Mrs. MiSun Park for her correction of the manuscript. References 1) L. A. Walton, “Zircaloy spacer grid design,” Trans. Am. Nucl. Soc., 32, 601–602 (1979). 2) J. G. Larson, “Optimization of the Zircaloy spacer grid design,” Trans. Am. Nucl. Soc., 43, 160–161 (1982). 3) I. G. Jang, Optimal Design of a Nuclear Fuel Rod Support Structure Based on Contact Stress Analysis, M. S. Thesis, Korea Atomic Energy Research Institute, (1999). 4) Y. H. Jung, K. N. Song, et al., Development of Advanced LWR Fuel: Development of Fuel Performance and Thermal Hydraulic Technology, KAERI/RR-2015/99, Korea Atomic Energy Research Institute (KAERI), (1999), [In Korean]. 5) K. N. Song, et al., Development Status and Research Directions on the Structural Components of the Fuel Assembly, KAERI/TR-865/97, Korea Atomic Energy Research Institute (KAERI), (1997), [In Korean]. 6) K. H. Yoon, et al., Mechanical/Structural Characteristic Test and FEA of a Spacer Grid Spring/Dimple for PWR Fuel Assembly, KAERI/TR-1763/2001, Korea Atomic Energy Research Institute (KAERI), (2001), [In Korean]. 7) K. H. Yoon, et al., Buckling Behavior Analysis of Spacer Grid by Lateral Impact Load, KAERI/TR1569/2000 , Korea Atomic Energy Research Institute (KAERI), (2000), [In Korean]. 8) K. H. Yoon, et al., Analysis of Buckling Behavior by Lateral Impact Load, KAERI/TR-1569/00, KAERI, (2000), [In Korean]. 9) K. H. Yoon, et al., “Shape optimization of the H-shape spacer grid spring structure,” J. Korean Nucl. Soci., 33[5], 547–555 (2001). 10) K. N. Song, et al., “Impact analysis of Dipper-type and Multi Spring-type fuel rod support grid assemblies in PWR,” Proc. 10th Int. Conf. on Nuclear Engineering, Arlington, VA, USA, Apr. 14–18, 2002, (2002). 11) K. N. Song, et al., “Shape optimization of a nuclear fuel rod support structure,” 16th Int. Conf. on Structural Mechanics in Reactor Technology, Washington, DC, U.S.A., Aug. 12–17, 2001, (2001). 12) K. H. Lee, K. H. Hwang, G. J. Park, “Robust design of a micro gyroscope using axiomatic approach,” 2000 U.S.–Korea Conf. on Science and Technology, Entrepreneurship, and Leadership, (2000).
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Design of a Spacer Grid Using Axiomatic Design 13) K. W. Lee, K. H. Lee, G. J. Park, “A structural optimization methodology using the independence axiom,” Proc. First Int. Conf. on Axiomatic Design ICAD2000, p. 145–150 (2000). 14) M. K. Shin, S. W. Hong, G. J. Park, “Axiomatic design of the motor driven tilt/telescopic steering system for safety and vibration,” Proc. Inst. Mech. Eng. (J. Automobile), 215[2], 179– 187 (2001). 15) N. P. Suh, Axiomatic Design, Oxford University Press, New York, (2001). 16) S. H. Do, G. J. Park, “Application of design axioms for glassbulb design and software development for design automation,” J. Mech. Des., 123[3], 322–329 (2001). 17) C. S. Shin, K. H. Lee, G. J. Park, “Robust structural optimization using design axioms in a discrete design space,” AIAA/USAF/NASA/ISSMO Symp. on Multidisciplinary Analysis and Optimization, AIAA-2000-4808, (2000). 18) ABAQUS/Standard Version 5.8 User’s Manual, Hibbitt, Karls-
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997 son, and Sorensen, Inc., Pawtucket, RI, (1998). 19) K. J. Bathe, Finite Element Procedures, Prentice-Hall, Englewood Cliffs, New Jersey, (1996). 20) GENESIS User Manual: Ver 5.0, VMA Engineering, (1998). 21) LS-DYNA User Manual, Livermore Software Technology, CO, (1999). 22) FEMBGENESIS User Manual: Ver 26.3D, VMA Engineering, (1996). 23) Taylor, J. E., Bendsoe, M. P., “An interpretation for min-max structural design problems including a method for relaxing constraints,” Int. J. Solid Struct., 20[4], 301–314 (1984). 24) G. N. Vanderplaats, Numerical Optimization Techniques for Engineering Design, McGraw-Hill Book Company, New York, (1984). 25) J. S. Arora, Introduction to Optimum Design, McGraw-Hill Book Company, New York, (1989).
