Method of Analysis

(3) Method of Analysis. All components of this vessel, and

basically the vessel itself, comprise bodies of revolution. For this reason,

it was decided to analyze the structure using a digital computer program

which is capable of determining stresses and displacements in shells of

revolution loaded by symmetric or nonsymmetric loads. The program used for

this problem is based on the multi-segment, numerical integration method as

applied to differential equations describing the general shell of revolution

boundary value problem. These shell parts may have the following shapes:

cylindrical, spheroidal, ellipsoidal, parabaloidal, conical, and toroidal.

For non-symmetric loadings, the loads must be broken down into their Fourier

components, each component requiring a computer run. There are many well

proven computer programs which generate extremely good solutions as compared

to exact or experimentally derived solutions, The designer must select the

computer program applicable to his problem and his available equipment.

The vessel was mathematically described by three models. Model No. 1 shown

here in Figure 2-14 includes both 4.0 inch diameter nozzles, the main

spherical shell and the cylindrical support skirt. Model No. 2, shown here

in Figure 2-15, includes the 40.0 inches diameter entranceway, the forged

reinforcement ring, the tori-spheroidal "door" and part of the main shell.

Model No. 3, shown here in Figure 2-16, includes the 10.0 inch diameter

penetration reinforcement plate and part of the main shell. The validity of

using these three models to accurately analyze the vessel rests upon the

relatively large distances (as measured along the spherical surfaces) between

any of the penetrations or attachments to the shell. For this spherical

shell, the decay length is approximately 17.0 inches. Decay length is

defined as that length along the shell in which a uniform moment applied to

an edge reduces to approximately zero. All penetrations and attachments are

spaced well beyond this distance.

(a) Model No. 1. This model, as shown in Figure 2-14 is

composed of 12 parts. These parts and their thicknesses are as follows:

Part No.

Type of Shell

Thickness, inches

1

Cylinder

0.25

2

Cylinder

0.25

3

Sphere

2.0

4

Sphere

Variable (to model the 1.0 inch

fillet radius on nozzle)

5

Torus

Variable (geometrically a

rectangular ring)

6

Cylinder

Variable (to model the 4.8 inch

radius transition zone)

7

Cylinder

0.1

8

Sphere

2.0

9

Sphere

(see 4 above)

10

Torus

(see 5 above)

11

Cylinder

(see 6 above)

12

Cylinder

0.1