判定票番号：PSN-2011-1207
文書番号：RS-5156502 Rev.0
1/2

24P098-P

Buckling Analysis of Gravity Support Legs for JT-60SA Vacuum Vessel
JT-60SA真空容器の重力支持脚座屈解析
Mitsuru Ejiri1, Kazunori Kitamura1, Takao Araki1, Junji Ohmori1, Shiro Asano1, Atsuro Hayakawa1
Yusuke K. Shibama2, Kei Masaki2, Akira Sakasai2
江尻 満1, 喜多村和憲1, 荒木隆夫1,大森順次1,浅野史朗1,早川敦郎1,
芝間祐介2、正木 圭2、逆井 章2
Toshiba Corporation,8, shinsugita-cho, isogo-ku,Yokohama, 235-8523, Japan1,
Japan Atomic Energy Agency, 801-1, mukoyama, Naka , 311-0193,Ibaraki, Japan2
株式会社 東芝, 〒235-8523 横浜市磯子区新杉田町81
独立行政法人 日本原子力研究開発機構, 〒311-0193 茨城県那珂市向山801-12
In the operation of tokamak, such loads as electromagnetic and seismic are assumed to be imposed on the vacuum
vessel (VV), and not a little thermal expansion takes place when VV is baked. The gravity support leg (GS) has tosupport the loads described above in addition to the dead weight of VV including in-vessel components and compensate
deformation. The GS is equipped with plate spring (PS) to have both stiffness and flexibility. In this study, the bucklingstrength of the PSs was evaluated. The effect of the initial imperfection of the PSs which is assumed to result frommachining or welding process on the buckling strength was also studied. It is concluded that GS has sufficient bucklingstrength against assumed initial imperfections.

1. Introduction
JT-60SA is a combined Japan-EU satellite
tokamak program. The manufacturing of VV andthe design of GS are making progress[1]. The
height and outer diameter of the VV are 6.6m and9.95m respectively. 9 GSs are installed in the bottomof VV toroidally in every 40 degrees. The buckling
analysis of GSs was carried out by using finite
element method.
2. Structure of GS and its FEM model
As is shown in Fig.1, a GS is divided into M210
bolt, stem, flanges and PSs and its height is about
2.5m. A plate spring consists of 9 plates whosethickness, width and height are 15mm, 600mm and500mm respectively. The PSs are picked up as theanalysis object out of the constituent components ofGS because of its weakest stiffness against buckling.
The mass of in-vessel components(270tons) is
distributed homogeneously into the wall of VV.

(a) VV and GSs（b） GS
Fig.1 Structure of GS and its FEM model

3. Analysis method and conditions
3.1 Method

We have adopted ABAQUS code(ver.6.6.3) for thisanalysis. The load at the proportionality collapse
point between applied load and resultant
displacement is defined as buckling load. Bucklingload is obtained by solving the eigenvalue buckling
equation (see eq.(1)). Each mode of deformation
corresponds to the eigenvalue of eq.(1). Obtained
buckling load divided by actual load is defined asload factor which is safety index against buckling.
According to the design criteria of bucklingstrength for the design conditions in the structuraldesign code of ASME[2], the load factor isprescribed to be larger than 3.
NMM[ K (NMb ) +λi K (Q ) ]φi = 0・・(1)Where,K (NMb ) ：the base state stiffness
K (NMQ ) ：the differential stiffness
λi：eigenvalue (refers to the ith mode)

φiM：eigenvector (refers to the ith mode)

3.2 Conditions
The initial and boundary conditions are as follows.
(1) Load condition
Horizontal direction: 3.3MN (seismic),Vertical direction: 14.2MN (seismic + electro-magnetic:10MN, dead weight:4.2MN)
As is shown in Fig.2, horizontal load is imposed in
the x direction. All GSs are arranged as the normalline of each PS passes through the torus center.
(2) Temperature condition (when baking)VV: 200deg., GS: 20deg.
(3) Boundary condition

判定票番号：PSN-2011-1207
文書番号：RS-5156502 Rev.0
2/2

The lower flange of the PS is fixed perfectly.
(4) Initial imperfection condition of PSs
Four types of initial imperfection pattern wereselected and analyzed as shown in Table 1. Except
for baking (ID.1), all initial imperfections of PSs are
imposed on GS03.
The shapes of initial imperfections are shown inFig.3. The bow-shaped deformation is imposed
according to the results obtained by the analysis forthe case without initial imperfection for ID.2～4.
GS03

GS04

GS02
GS05

4.2 With initial imperfection
Obtained load factors and according decrease ratecompared with the load factor (8.31) in the casewithout initial imperfection are presented in Table 2.
－Buckling was not observed in the GS03 but in theGS08. Imposed load may be redistributed among 8GSs besides GS03. The GS positioned
symmetrically to the x-axis is buckled because it issusceptible to be buckled owing to its angle to theloading direction.
－Obtained decrease rates are small, and even if oneof the GSs is assumed not to work, buckling strengthis within the design criteria (see Fig.4).

Y

Table 2 Analysis results
GS01
XID

Load Factor

Ref

8.31

Loading direction
GS06
GS09
GS07

GS08

IDGS
Location

Ref
1GS01～
GS09

2GS03

3GS03

4

Number ofDisplacement
PSs
Without imperfection
81
About 10mm
(9×9)
110mm(outermost)
2mm and920mm

GS03

9-8.063%28.31

no decrease

38.30～7.94

46.80

GS08 PS

0% ～4%
18%

Loading direction
GS03 does not work
GS01

Direction
ZX

outwardly
outwardly
outwardly

1GS is assumed not to work.
(The GS03 is deleted from theFEM model.)Displacement

Displacement

GS03 PS or
GS08 PSdecrease rate

1Fig.2 GS arrangement and loading direction
Table.1 Analysis cases (imperfection patterns of PSs)

Buckling
Location

Plate Spring
Sine Curve

Plate Spring(a) Baking(ID.1)(b) Except for baking(ID.2～4)
Fig.3 Shape of initial imperfection

4. Results
4.1 Without initial imperfection
The minimum load factor was 8.31 and wasobserved in GS03 or GS08.
All buckling modes are surveyed in which loadfactor is less than 20. Buckling took place at the PSs
in all modes.

YGS08
Load factor: 6.80Design Criteria : 3.0

Fig 4 Buckling mode for ID.4 (1GS is assumed not to work)

5. Conclusion
As the results of FEM analysis, it is concluded that
GS has sufficient strength against buckling asfollows.
Several types of initial imperfections are assumedto take place in the PSs. Calculated load factors
decrease only several percents compared with that ofwithout initial imperfection case. Even if one of theGSs does not work, the decrease rate is 18%.
In the analyzed cases, obtained all load factors arelarger than 3 and are within the design criteriaprescribed in the structural design code of ASME[2].
References[1] Y.K.Shibama et al.,“Manufacturing status of JT-60SA
vacuum vessel and the related technology of welding”,
Proceedings of 2011 ASME Pressure Vessels andPiping Conference, Baltimore, Maryland (2011)[2] ASME SEC.III-NH, Appendices-T(2007).