An Analysis of Shell Structure for Dead Load

H.M. FanPPPL

September 16, 2005

Purposes of Analysis

• Provide a quick look at the dead load responses of a base support system using the existing FEA model.

• Examine the stress and deformation patterns of the shell structure

• Explore the normal stress and the shear stress distribution at the bolt joints

FEA Model• FEA model simulates one field period.

• Cyclically boundary conditions were applied (see next slide).

• Geometry of the shell structure are imported from Pro/E CAD modeling, which was provided by ORNL

• Small features in the geometry were removed to improve meshing of model.

• Model includes shells with tees and wings, wing bags, poloidal break spacers, and toroidal flange spacers. Modular coils and clamp assembly are not included.

• All contact surfaces are assumed to be bonded and the structure acts linearly.

• Vertical and toroidal displacement constraints were placed on the lower vertical stiffeners at the middle four-degree regions of the shell type C.

Upper shell C

Upper shell B

Upper shell A

Lower shell A

Lower shell B

Lower shell C

Boundary Conditions• Cyclic symmetry between toroidal spacers at -60° and +60° (see Fig.A)

• Cyclic symmetry for wing bags outside the 120° limits and their rotational images (see Fig.B)

• Rotational images were bonded to the shell

Figure AFigure B

Rotational images

Material Properties and Dead Load Distribution

• Isotropic smeared material property was assumed for all elements.

• Total vertical load of 341620 Newtons (or 76800 pounds) was applied at the vertical stiffeners.

• The vertical load was equally divided on the upper and lower stiffeners. The load on the inboard stiffener is one half of the load on the outboard stiffener.

• Because of the partial vertical stiffener provided on shell Type B, the load distribution on was assumed as:

Shell type A: 1/3

Shell type B: 1/6

Shell type C: 1/2

• The following material properties are used:

  E (MPa) CTE (m/m/°C) Poisson's Ratio

Tee/shell 145,000.00 1.70E-05 0.31

Toroidal spacer 150,000.00 1.70E-05 0.27

poloidal spacer 193,000.00 1.70E-05 0.31

Wing bag 13,750.00 3.00E-05 0.32

Wing bag image 689.00 3.00E-05 0.32

Vertical Displacements Uz

Unit of displacement in meter

• The contour plot shows that the vertical displacements at the outboard region are much larger than the displacements at the inboard region. It is primary due to the location of the center of gravity of the dead load as well as the unequal spans between the base supports.

• The dead load cause twisting on the shell structure

• The displacements are not quite symmetry between the same type of shell because the shells with tee-shape beams, poloidal breaks, and the openings are rotational symmetry with respect to the middle span.

• Displacements are higher in the mid-span. The maximum vertical displacement at the stiffener is due to opening underneath.

Maximum Displacement

Von Mises Stresses

Unit of stress in pascal

Top ViewView from Bottom

Some Local High Stress Regions

Shell type B

12.2 MPa

Shell type A

8.0 MPa

21.3 MPa

Shell type C

• Higher stresses are found in the vicinity of openings

• Stresses are higher in shell type C and lesser in shell type A

Stresses in Shell Do Not Follow the Simple Beam Bending Behavior

Sell stress in the toroidal direction

• Because: (a) It is a tube structure with very large radius/thickness ratio; (b) The openings change the load paths; (c) It is a curve member.

• In the outboard region, the large openings change the load carrying pattern. Toroidal tensions were found above the openings in shell type A and B

• All dead loads are carried down to the supports in shell type C, for which it undertakes higher stress than shell types A and B.

• At the mid-span, the toroidal stress, Sy, plot shows compression in the top elements and tension in the bottom elements.

• In shell type C, It shows tension in the top elements and compression in the bottom elements (see plots in next page)

• For viewing clarity, the contour plot range was changed to a small values.

More Stress Sy Plots

View from Top

View from Bottom

View from Center

• At the inboard region, where no spaces are available for bolt connections, the toroidal tensile stress is very small except joint C-C (see slide of contact pressure on C-C ).

Contact Stresses on Flange Bolt Joints

Contact pressure

Contact shear stress

Stress unit in pascal

• Positive contact pressure indicates load toward the surface and therefore is in compression• For viewing clarity, the contour plot range was changed to a small values.

Contact Stresses on Flange Bolt Joints A-A

Contact pressure

• Positive contact pressure is in compression• Both the normal pressure and the shear stress in the flange bolt joints are greater near the openings

Contact shear stress

Stress unit in pascal

Contact Stresses on Flange Bolt Joints A-BContact

shear stressContact pressure

Stress unit in pascal

Note – Positive contact pressure indicates load toward the surface and therefore is in compression

Contact Stresses on Flange Bolt Joints B-C

Contact pressure

Contact shear stress

Stress unit in pascal

• Positive contact pressure indicates stress in compression• Maximum shear stress occurs at the roots of the vertical stiffeners

Contact Stresses on Flange Bolt Joints C-C

Contact pressure

Stress unit in pascal

Contact shear stress

Contact Pressure on Poloidal Breaks Shell Type C

Shell Type BShell Type A

Unit of pressure in pascal

Note – Positive pressure indicates load toward the surface and therefore is in compression

Contact Shear Stress on Poloidal Breaks Shell Type A Shell Type C

Shell Type B

Unit of pressure in pascal

• Maximum shear stresses occur at the corners of poloidal breaks

• Wing bag images were created to form an appropriate cyclic symmetry boundary condition . The stiffness of the wing bag image was set at two percent of the material property of wing bag.

• The dead load distribution is approximate. A more accurate dead load distribution shall base on the real geometry with gravity loads.

• The net reactions at displacement constraints are Fx = -17470 N, Fy = 2004 N and Fz = 341620 N. However, only vertical load of 341620 Newtons was applied.

• The shell structure is bending and twisting between base supports.

• Maximum stress, ~21 MPa, occurs locally at lead opening and the base support interface in the shell type C. In general, stresses are higher near openings and in the shell type C. The stresses in most areas are less than 7 MPa.

• More tension across the lower flange bolt joints A-A and upper flange bolt joints B-C and C-C.

• In the inboard region, where no spaces are available for bolt connections, the toroidal tensile stress is small except joint C-C.

• The result accuracy is lowly at elements in joint C-C due to large element aspect ratio.

Discussion and Summary

• Because of base support at shell type C, the flange bolt joints, B-C and C-C expose to bigger shear stress. The maximum shear stresses occur at the roots of the vertical stiffeners called “feet”.

• Both the normal pressure and shear stress in the flange bolt joints are greater near the openings

• The linear analysis results in the maximum displacement of 0.174 mm and the maximum vertical displacement is 0.169 mm.

• The displacements of the shell are not symmetry because tee-shape beam, openings and poloidal breaks are not symmetry.

• For dead load, the tensile stress at the poloidal break in small. They are usually peak at the edges. The shear stress and the compressive stress are the main stresses to carry the force through the joints.

• The peak shear stresses in the poloidal break joints occur at the corners of the joints.

• Change the base support location will change the stress and deflection pattern of the shell structure and the forces across the bolt joints.

Discussion and Summary (Continued)