V. Spherical Shell Displacements

To find the displacement in the direction of the load due to a unit load applied at the quadrants of a quarter of a spherical shell.

Reference

MacNeal, R.H. and Harder, R.C., A Proposed Standard Set of Problems to Test Finite Element Accuracy, Finite Element in Analysis and Design 1, 1985.

Problem

For the quarter of a spherical shell find the displacement in the direction of the load.

 E = 6.825(10)7 psi

 Poisson’s ratio = 0.3

 t = 0.04 inches

 r = 10 in.

Boundary conditions:

• Vertical restraint at center of free edge
• Symmetry defines boundary conditions

Comparison

Table 1. Comparison of results
Deflection, δ (in) 0.094 0.09342 <1%

Tip: You can copy and paste this content directly into a .std file to run in STAAD.Pro.

The file C:\Users\Public\Public Documents\STAAD.Pro CONNECT Edition\Samples\ Verification Models\04 Plates Shells\Spherical Shell Displacements.STD is typically installed with the program.

``````STAAD SPACE :A QUARTER OF A SHERICAL SHELL
START JOB INFORMATION
ENGINEER DATE 14-Sep-18
END JOB INFORMATION
*
* REFERENCE: MACNEAL AND HARDER, A PROPOSED STANDARD SET OF PROBLEMS
*            TO TEST FINITE ELEMENT ACCURACY,
*            FINITE ELEMENT IN ANALYSIS AND DESIGN 1, NORTH HOLLAND
*            1985
*
INPUT WIDTH 72
UNIT INCHES POUND
JOINT COORDINATES
1 10 0 0; 2 0 0 10; 3 1.951 0 9.808; 4 3.827 0 9.239; 5 5.556 0 8.315;
6 7.071 0 7.071; 7 8.315 0 5.556; 8 9.239 0 3.827; 9 9.808 0 1.951;
10 9.877 1.564 0; 11 0 1.564 9.877; 12 1.927 1.564 9.687;
13 3.78 1.564 9.125; 14 5.487 1.564 8.212; 15 6.984 1.564 6.984;
16 8.212 1.564 5.487; 17 9.125 1.564 3.78; 18 9.687 1.564 1.927;
19 9.511 3.09 0; 20 0 3.09 9.511; 21 1.856 3.09 9.328;
22 3.64 3.09 8.787; 23 5.284 3.09 7.908; 24 6.725 3.09 6.725;
25 7.908 3.09 5.284; 26 8.787 3.09 3.64; 27 9.328 3.09 1.855;
28 8.91 4.54 0; 29 0 4.54 8.91; 30 1.738 4.54 8.739; 31 3.41 4.54 8.232;
32 4.95 4.54 7.408; 33 6.3 4.54 6.3; 34 7.408 4.54 4.95;
35 8.232 4.54 3.41; 36 8.739 4.54 1.738; 37 8.09 5.878 0;
38 0 5.878 8.09; 39 1.578 5.878 7.935; 40 3.096 5.878 7.474;
41 4.495 5.878 6.727; 42 5.721 5.878 5.72; 43 6.727 5.878 4.495;
44 7.474 5.878 3.096; 45 7.935 5.878 1.578; 46 7.071 7.071 0;
47 0 7.071 7.071; 48 1.379 7.071 6.935; 49 2.706 7.071 6.533;
50 3.928 7.071 5.879; 51 5 7.071 5; 52 5.879 7.071 3.928;
53 6.533 7.071 2.706; 54 6.935 7.071 1.379; 55 5.878 8.09 0;
56 0 8.09 5.878; 57 1.147 8.09 5.765; 58 2.249 8.09 5.431;
59 3.266 8.09 4.887; 60 4.156 8.09 4.156; 61 4.887 8.09 3.266;
62 5.431 8.09 2.249; 63 5.765 8.09 1.147; 64 4.54 8.91 0;
65 0 8.91 4.54; 66 0.886 8.91 4.453; 67 1.737 8.91 4.194;
68 2.522 8.91 3.775; 69 3.21 8.91 3.21; 70 3.775 8.91 2.522;
71 4.194 8.91 1.737; 72 4.453 8.91 0.886; 73 3.09 9.511 0;
74 0 9.511 3.09; 75 0.603 9.511 3.031; 76 1.182 9.511 2.855;
77 1.717 9.511 2.569; 78 2.185 9.511 2.185; 79 2.569 9.511 1.717;
80 2.855 9.511 1.182; 81 3.031 9.511 0.603;
ELEMENT INCIDENCES SHELL
1 2 3 12 11; 2 3 4 13 12; 3 4 5 14 13; 4 5 6 15 14; 5 6 7 16 15;
6 7 8 17 16; 7 8 9 18 17; 8 9 1 10 18; 9 11 12 21 20; 10 12 13 22 21;
11 13 14 23 22; 12 14 15 24 23; 13 15 16 25 24; 14 16 17 26 25;
15 17 18 27 26; 16 18 10 19 27; 17 20 21 30 29; 18 21 22 31 30;
19 22 23 32 31; 20 23 24 33 32; 21 24 25 34 33; 22 25 26 35 34;
23 26 27 36 35; 24 27 19 28 36; 25 29 30 39 38; 26 30 31 40 39;
27 31 32 41 40; 28 32 33 42 41; 29 33 34 43 42; 30 34 35 44 43;
31 35 36 45 44; 32 36 28 37 45; 33 38 39 48 47; 34 39 40 49 48;
35 40 41 50 49; 36 41 42 51 50; 37 42 43 52 51; 38 43 44 53 52;
39 44 45 54 53; 40 45 37 46 54; 41 47 48 57 56; 42 48 49 58 57;
43 49 50 59 58; 44 50 51 60 59; 45 51 52 61 60; 46 52 53 62 61;
47 53 54 63 62; 48 54 46 55 63; 49 56 57 66 65; 50 57 58 67 66;
51 58 59 68 67; 52 59 60 69 68; 53 60 61 70 69; 54 61 62 71 70;
55 62 63 72 71; 56 63 55 64 72; 57 65 66 75 74; 58 66 67 76 75;
59 67 68 77 76; 60 68 69 78 77; 61 69 70 79 78; 62 70 71 80 79;
63 71 72 81 80; 64 72 64 73 81;
ELEMENT PROPERTY
1 TO 64 THICKNESS 0.04
DEFINE MATERIAL START
ISOTROPIC MATERIAL1
E 6.825e+07
POISSON 0.3
END DEFINE MATERIAL
CONSTANTS
MATERIAL MATERIAL1 ALL
SUPPORTS
1 10 19 28 37 46 55 64 73 FIXED BUT FX FY MZ
2 11 20 29 38 47 56 65 74 FIXED BUT FY FZ MX
6 FIXED BUT FX FZ MX MY MZ
2 FZ 1
1 FX -1
PERFORM ANALYSIS
PRINT JOINT DISPLACEMENTS LIST 1 2
FINISH
``````

```   JOINT DISPLACEMENT (INCH RADIANS)    STRUCTURE TYPE = SPACE