# SS-V: 5070 Pinched Hemispherical Shell

Test No. VNL08 Find displacements of a hemispherical shell loaded with inward and outward concentrated forces.

## Definition

A hemispherical shell is loaded with inward and outward concentrated forces at point
A and point B, respectively. The hemisphere has an 18 degree hole at the top and the
quadrant of the hemisphere is modeled utilizing symmetric boundary conditions (Figure 1). Correspondingly, forces P shown in
Figure 1 are acting on the quadrant.
Displacement at points A and B are to be determined for force values P = 40, 60, and
100 lbf.

The material properties are:

**Properties****Value**- Modulus of Elasticity
- 6.825e+7 psi
- Poisson's Ratio
- 0.3

## Results

Symmetry conditions were simulated via sliding boundary conditions applied at faces coinciding with symmetry planes (Figure 2). Concentrated forces were applied in points of outer face of the sphere (Figure 3). In order to eliminate rigid body motion along Z-axis a point on the top of the sphere was constrained in Z-direction (Figure 4).

The following tables summarize
the comparison results.

Load [lbf] | Ref Solution *, Ux at Point A [in] | SimSolid, Displacement Uy at Point A [in] | % Difference |
---|---|---|---|

40 | -3.280 | -3.148 | -4.02% |

60 | -4.360 | -4.120 | -5.50 |

100 | -5.950 | -5.482 | -7.87 |

Load [lbf] | Ref Solution *, Uy at Point B [in] | SimSolid, Displacement Ux at Point B [in] | % Difference |
---|---|---|---|

40 | -2.330 | -2.268 | -2.66% |

60 | -2.830 | -2.725 | -3.71% |

100 | -3.430 | -3.255 | -5.10% |

* Ref Solution is a thin shell model

^{1}Test 3DNLG-9 from NAFEMS Publication R0024 “A Review of Benchmark Problems for Geometric Non-linear Behaviour of 3-D Beams and Shells (SUMMARY).”